I have based this on US Eastern time and GMT. Most of this info is courtesy of the www.timeanddate.com site.

 5:00am EST Dec 31st (10AM GMT Dec 31st) - Kiritimati on the Christmas Islands, in Kirimati, and Tonga in the Pacific are the first to celebrate year 2000 Places: Kiritimati (Kiribati - Christmas Islands), Nukualofa (Tonga)

 5:15am EST Dec 31st (10:15AM GMT Dec 31st) - Chatham Island outside of New Zealand has a special timezone and seems to be the second place on earth to see the clocks go to year 2000 Places: Chatham Island (New Zealand)

 6:00am EST Dec 31st (11:00AM GMT Dec 31st) - New Zealand, the South Pole base and Fiji are next to go. Places: Suva (Fiji Islands), Wellington (New Zealand), Auckland (New Zealand), Rawaki (Kiribati - Phoenix Islands)

 7:00am EST Dec 31st (12:00PM GMT Dec 31st) - Eastern Russia, some Pacific islands Places: Anadyr (Russia), Kamchatka (Russia), Makwa (Nauru), Funafuti (Tuvalu), Tarawa (Kiribati), Majuro (Marshall Islands)
 

 7:30am EST Dec 31st (12:30PM GMT Dec 31st) - Norfolk Island - Australia Places: Kingston (Australia - Norfolk Island)

 8:00am EST Dec 31st (1:00PM GMT Dec 31st) - Parts of eastern Australia and some pacific Islands Places: Sydney (Australia), Melbourne (Australia), Canberra (Australia), Vila (Vanuatu), Kolonia (Fed. states of Micronesia), Honiara (Solomon Islands), Noumea (France - New Caledonia), Lord Howe Island (Australia), Hobart (Australia - Tasmania)

 8:30am EST Dec 31st (1:30PM GMT Dec 31st) - South Australia Places: Adelaide (Australia)

 9:00am EST Dec 31st (2:00PM GMT Dec 31st) - Queensland - Australia, a part of Russia and some islands far east in the Pacific Places: Brisbane (Australia), Vladivostok (Russia), Port Moresby (Papua New Guinea), Guam (U.S.A. - Mariana Islands)

 9:30am EST Dec 31st (2:30PM GMT Dec 31st) - Northern Territory - Australia Places: Darwin (Australia)

 10:00am EST Dec 31st (3:00PM GMT Dec 31st) - Now Japan, Korea and far east Indonesia enters year 2000 Places: Tokyo (Japan), Seoul (South Korea), ÷saka (Japan), Yokohama (Japan), Taegu (South Korea), Sapporo (Japan), Pusan (South Korea), Nagoya (Japan), K–be (Japan), Ky–to (Japan), Kitaky¸sh¸ (Japan), Kawasaki (Japan), Inch'on (South Korea),
Fukuoka (Japan), Pyongyang (North Korea), Ternate (Indonesia - Halmahera), Ambon (Indonesia - Seram), Jayapura (Indonesia - Irian Jaya)

 11:00am EST Dec 31st (4:00PM GMT Dec 31st) - China, parts of South-East Asia, Central Indonesia and rest of Australia Places: Beijing (China), Taipei (Taiwan), Shanghai (China), Singapore (Singapore), Manila (Philippines), Hong Kong (China), Perth (Australia), Kuala Lumpur (Malaysia), Ulaanbaatar (Mongolia), Bandar Seri Begawan (Brunei), Zibo (China), Zhenghou (China), Wuhan (China), Tsingtao (China), Tientsin (China), Tangshan (China), Taiyuan (China), Sian (China), Shijiazhuang
(China), Qiqihar (China), Nanchang (China) and many more...

 12:00pm EST Dec 31st (5:00PM GMT Dec 31st) - Indonesia and rest of South-East Asia Places: Hanoi (Vietnam), Bangkok (Thailand), Jakarta (Indonesia - Java), Surabaya (Indonesia - Java), Krasnoyarsk (Russia), Vientiane (Laos), Saigon (Vietnam), Phnomh Penh (Cambodia), Palembang (Indonesia - Sumatera), Medan (Indonesia - Sumatera), Malang (Indonesia
- Java), Bandung (Indonesia - Java), Surakarta (Indonesia - Java), Semarang (Indonesia - Java), The Settlement (Australia - Christmas Island)

 12:30pm EST Dec 31st (5:30PM GMT Dec 31st) - Burma with it's half-hour timezone Places: Rangoon (Burma)

 1:00pm EST Dec 31st (6:00PM GMT Dec 31st) - Bangladesh, Sri Lanka and parts of Russia Places: Dhaka (Bangladesh), Colombo (Sri Lanka), Almaty (Kazakhstan), Novosibirsk (Russia), Omsk (Russia), Thimphu (Bhutan), Chittagong (Bangladesh)

 1:15pm EST Dec 31st (6:15PM GMT Dec 31st) - Nepal has it's special timezone here Places: Kathmandu (Nepal)

 1:30pm EST Dec 31st (6:30PM GMT Dec 31st) - All of India enters year 2000 Places: New Delhi (India), Calcutta (India), Mumbai (India), Delhi (India), N“gpur (India), Chennai (India), Lucknow (India), K“npur (India), Jaipur (India), Hyder“b“d (India), Bangalore (India), Ahmad“b“d (India)

 2:00pm EST Dec 31st (7:00PM GMT Dec 31st) - Most of Pakistan, Uzbekistan, Turkmenistan, Kyrgystan and parts of Russia are next Places: Tashkent (Uzbekistan), Islamabad (Pakistan), Karachi (Pakistan), Lahore (Pakistan), Chelyabinsk (Russia), Sverdlovsk (Russia), Perm (Russia), Ufa (Russia), Faisalabad (Pakistan), Ashkhabad (Turkmenistan), Dushanbe
(Tajikistan), Bishkek (Kyrgyzstan), Male (Maldives), Port-aux-Francais (France - Kerguelen)

 2:30pm EST Dec 31st (7:30PM GMT Dec 31st) - Afghanistan Places: Kabul (Afghanistan)

 3:00pm EST Dec 31st (8:00PM GMT Dec 31st) - Armenia, Azerbaijan, parts of Russia and Arabia, some islands in the Indian Ocean. Places: Dubai (United Arab Emirates), Tbilisi (Georgia), Yerevan (Armenia), Baku (Azerbaijan), Samara (Russia), Port Louis (Mauritius), Abu Dhabi (United Arab Emirates), Muscat (Oman), Victoria (Seychelles), Saint-Denis
(Reunion)

 3:30pm EST Dec 31st (8:30PM GMT Dec 31st) - Iran Places: Tehran (Iran)

 4:00pm EST Dec 31st (9:00PM GMT Dec 31st) - Most of western Asia and Arabia, parts of Russia, and eastern parts of Africa Places: Moscow (Russia), Baghdad (Iraq), Nairobi (Kenya), Addis Ababa (Ethiopia), Aden (Yemen), Riyadh (Saudi Arabia), Antananarivo (Madagaskar), Kuwait City (Kuwait), Ad Dawhah (Qatar), Dar es Salaam (Tanzania), Sana (Yemen),
Kazan (Russia), Novgorod (Russia), Sankt-Peterburg (Russia), Murmansk (Russia), Mogadishu (Somalia), Makkah (Saudi Arabia), Al Manamah (Bahrain), Asmera (Eritrea), Djibouti (Djibouti), Jiddah (Saudi Arabia) and many more...

 5:00pm EST Dec 31st (10:00PM GMT Dec 31st) - Israel, Eastern Europe and Turkey, parts of Africa - from North to South. Places: Cairo (Egypt), Bucharest (Romania), Athens (Greece), Sofia (Bulgaria), Ankara (Turkey), Khartoum (Sudan), Johannesburg (South Africa), Harare (Zimbabwe), Cape Town (South Africa), Beirut (Lebanon), Minsk (Belarus), Tallinn
(Estonia), Jerusalem (Israel), Amman (Jordan), Istanbul (Turkey), Helsinki (Finland), Nicosia (Cyprus), Tel Aviv (Israel), Vilnius (Lithuania), Riga (Latvia), Damascus (Syria), Alexandria (Egypt), Kiev (Ukraine), Pretoria (South Africa), Tripoli (Libya), Kishinev (Moldova), Izmir (Turkey) and many more...

 6:00pm EST Dec 31st (11:00PM GMT Dec 31st) - Western Europe, parts of Africa Places: Brussels (Belgium), Geneva (Switzerland), Copenhagen (Denmark), Budapest (Hungary), Berlin (Germany), Barcelona (Spain), Z¸rich (Switzerland), Warsaw (Poland), Vienna (Austria), Stockholm (Sweden), Rome (Italy), Paris (France), Amsterdam (The Netherlands),
Madrid (Spain), Algiers (Algeria), Lagos (Nigeria), Frankfurt (Germany), Belgrade (Yugoslavia - Serbia), Zagreb (Croatia), Prague (Czech Republic), Oslo (Norway), Gibraltar (U.K. - Gibraltar), D¸sseldorf (Germany), Bratislava (Slovakia), Skopje (Macedonia), Luxembourg (Luxembourg), Hamburg (Germany), Tirane (Albania), Bern (Switzerland), Venice (Italy), Turin (Italy), Tunis (Tunisia), Palma (Spain), Nice (France), Naples (Italy), Munich (Germany), Kinshasa (Zaire), Kano Nigeria (Nigeria), Podgoriza (Yugoslavia - Montenegro) and many more...

 7:00pm EST Dec 31st (12:00 AM GMT Jan 1st, 2000) - UTC-time, London, Portugal, Iceland, western Africa. Places: London (U.K. - England), Dublin (Ireland), Casablanca (Morocco), Lisbon (Portugal), Reykjavik (Iceland), Glasgow (U.K. - Scotland), Porto (Portugal), Birmingham (U.K. - England), Dakar (Senegal), Bamako (Mali), Tanger (Morocco), Rabat
(Morocco), Nouakchott (Mauritania), Freetown (Sierra Leone), Conakry (Guinea), Accra (Ghana), Liverpool (U.K. - England), Ouagadougou (Burkina Faso), Monrovia (Liberia), Lome (Togo), Abidjan (Cote D'Ivoire) and many more...

 8:00pm EST Dec 31st (1:00 AM GMT Jan 1st, 2000) - Azores in the middle of the Atlantic Ocean Places: Azores (Portugal), Praia (Cape Verde)

 9:00pm EST Dec 31st (2:00 AM GMT Jan 1st, 2000) - Eastern parts of South-America Places: Sao Paulo (Brazil), Rio de Janeiro (Brazil), Brasilia (Brazil), Salvador (Brazil), Salvador (Brazil), Recife (Brazil), Fernando de Noronha (Brazil)

 10:00pm EST Dec 31st (3:00 AM GMT Jan 1st, 2000) - Rest of eastern South-America Places: Buenos Aires (Argentina), Santiago (Chile), Asuncion (Paraguay), Montevideo (Uruguay), Nuuk (Denmark - Greenland), Stanley (U.K. - Falkland Islands), Cayenne (France - French Guiana), Paramaribo (Suriname)

 10:30pm EST Dec 31st (3:30 AM GMT Jan 1st, 2000) - Newfoundland in Canada Places: St. John's (Canada - Newfoundland)

 11:00pm EST Dec 31st (4:00 AM GMT Jan 1st, 2000) - Eastern Canada, many Caribbean islands, parts of South-America Places: Caracas (Venezuela), Halifax (Canada - Nova Scotia), Santo Domingo (Dominican Republic), San Juan (Puerto Rico), La Paz (Bolivia), Port of Spain (Trinidad and Tobago), Bermuda (U.K. - Bermuda), Manaus (Brazil), Georgetown (Guyana),
Bridgetown (Barbados), Saint John (Canada - New Brunswick), Roseau (Dominica), Charlottetown (Canada - Pr.Edward I), Kingstown (Saint Vincent and the Grenadines), Castries (Saint Lucia), Basseterre (Saint Kitts and Nevis), Willemstad (The Netherlands - Netherlands Antilles), Plymouth (U.K. - Montserrat), Fort-de-France (France - Martinique), Basse-Terre (France - Guadeloupe), Saint George's (Grenada) and many more...

 12:00 am EST Jan 1st, 2000 (5:00 AM GMT Jan 1st, 2000) - Eastern Time in Canada and USA, Western South-America Places: Washington DC (U.S.A.), New York (U.S.A. - New York), Havana (Cuba), Detroit (U.S.A. - Michigan), Toronto (Canada - Ontario), Montreal (Canada - Quebec), Lima (Peru), Boston (U.S.A. - Massachusetts), Bogota (Colombia), Atlanta (U.S.A. - Georgia), Ottawa (Canada - Ontario), Nassau (Bahamas), Kingston (Jamaica), Indianapolis (U.S.A. - Indiana), Hartford (U.S.A. - Connecticut), Guayaquil (Ecuador), Columbia (U.S.A. - South Carolina), Louisville (U.S.A. - Kentucky), Tampa (U.S.A. - Florida), Richmond (U.S.A. - Virginia), Raleigh (U.S.A. - North Carolina), Philadelphia
(U.S.A. - Pennsylvania), Panama (Panama), Quito (Ecuador), Quebec (Canada - Quebec), Miami (U.S.A. - Florida), Medellin (Colombia), Albany (U.S.A. - New York), Harrisburg (U.S.A. - Pennsylvania) and many more...

 1:00 am EST Jan 1st, 2000 (6:00 AM GMT Jan 1st, 2000) - Central Time in Canada and USA, Mexico and most of Latin America Places: Mexico City (Mexico), Guatemala (Guatemala), Chicago (U.S.A. - Illinois), Montgomery (U.S.A. - Alabama), Winnipeg (Canada - Manitoba), Tegucigalpa (Honduras), San Salvador (El Salvador), St. Paul (U.S.A. - Minnesota), New Orleans (U.S.A. - Louisiana), Minneapolis (U.S.A. - Minnesota), Managua (Nicaragua), Houston (U.S.A. - Texas), Aguascalientes (Mexico), Des Moines (U.S.A. - Iowa), Dallas (U.S.A. - Texas), Jackson (U.S.A. - Mississippi), Kansas City (U.S.A. - Missouri), Baton Rouge (U.S.A. - Louisiana), Acapulco (Mexico), Veracruz (Mexico), Topeka (U.S.A. - Kansas), Austin (U.S.A. - Texas), Santa Ana (El Salvador), San Jose (Costa Rica), Regina (Canada - Saskatchewan), Oklahoma City (U.S.A. - Oklahoma), Nashville (U.S.A. - Tennessee), Madison (U.S.A. - Wisconsin),
Little Rock (U.S.A. - Arkansas), Lincoln (U.S.A. - Nebraska), Leon (Mexico), Jefferson City (U.S.A. - Missouri), Iqaluit (Canada - Nunavut Territory) and many more...

 2:00 am EST Jan 1st, 2000 (7:00 AM GMT Jan 1st, 2000) - Mountain Time in Canada and USA Places: Edmonton (Canada - Alberta), Denver (U.S.A. - Colorado), Phoenix (U.S.A. - Arizona), Aklavik (Canada - Northwest Territories), Yellowknife (Canada - Northwest Territories), Salt Lake City (U.S.A. - Utah), Mazatlan (Mexico), Santa Fe (U.S.A. - New Mexico),
Helena (U.S.A. - Montana), Chihuahua (Mexico), Calgary (Canada - Alberta), El Paso (U.S.A. - Texas), Albuquerque (U.S.A. - New Mexico), Tucson (U.S.A. - Arizona), Mesa (U.S.A. - Arizona), Aurora (U.S.A. - Colorado), Cheyenne (U.S.A. - Wyoming), Boise (U.S.A. - Idaho)

 3:00 am EST Jan 1st, 2000 (8:00 AM GMT Jan 1st, 2000) - Pacific Time in Canada and USA Places: Los Angeles (U.S.A. - California), San Francisco (U.S.A. - California), Vancouver (Canada - Brit. Columbia), Seattle (U.S.A. - Washington), San Diego (U.S.A. - California), Whitehorse (Canada - Yukon), Oakland (U.S.A. - California), San Jose (U.S.A. - California), Tijuana (Mexico), Sacramento (U.S.A. - California), Mexicali (Mexico), Las Vegas (U.S.A. - Nevada), Carson City (U.S.A. -
Nevada), Salem (U.S.A. - Oregon), Long Beach (U.S.A. - California), Stockton (U.S.A. - California), Riverside (U.S.A. - California), Anaheim (U.S.A. - California), Adamstown (U.K. - Pitcairn), Portland (U.S.A. - Oregon)

 4:00 am EST Jan 1st, 2000 (9:00 AM GMT Jan 1st, 2000) - Alaska - USA Places: Anchorage (U.S.A. - Alaska), Fairbanks (U.S.A. - Alaska), Nome (U.S.A. - Alaska), Juneau (U.S.A. - Alaska)

 5:00 am EST Jan 1st, 2000 (10:00 AM GMT Jan 1st, 2000) - Hawaii - USA, Tahiti and Cook Islands Places: Honolulu (U.S.A. - Hawaii), Rarotonga (Cook Islands), Papeete (France - French Polynesia-Tahiti), Aleutian Islands (U.S.A. - Alaska)

 6:00 am EST Jan 1st, 2000 (11:00 AM GMT Jan 1st, 2000) - Western Samoa Places: Apia (Samoa)