Connected to Singapore by two land bridges, the peninsular western Malaysia is the most easily accessible to Singapore. You can drive, fly or take a boat out to Malaysia. Malaysia is a relaxed country steeped in culture and famous for its culinary enthusiasm. Malacca and Kuala Lumpur are popular 1-2 day getaways from Singapore. Well worth visiting is Pulau Tioman (45 minute direct flight or four hour boat ride from Singapore), with natural rainforests and mountainous terrain, beautiful beaches and good scuba diving. Other islands worth discovering include the islands of Pulau Redang Pulau Perhentian and Pulau Sibu (mainly for beaches and diving), and Pulau Penang (well known for its food).
Malaysia (East)
East Malaysia is a place for nature lovers. One of the tallest peaks of the region, Kota Kinabalu, soars over 12,000 feet above sea level, and makes for a wonderful two to three day mountain hike. Borneo offers exotic rain-forest trekking and wildlife. Some of the islands off the coast offer some of the world's best diving (e.g. Pulau Sipadan, off the coast of Sabah).
Thailand
Thailand is the land of smiles and of Buddhist temples, royal ruins and rich culture. Bangkok is an international shopping, cultural and entertainment center. Thailand also boasts some of the finest tropical islands easily accessible either by direct flight from Singapore or via Bangkok.
Indonesia
Indonesia (including Sumatra) is a vast and varied country where you can visit sacred temple sites (Borobudur), lively arts and cultural centers (Jogjakarta) and beautiful islands (e.g. Bali, Bintan, Batam).
Cambodia
Cambodia , is a unique place offering unparalleled glimpses of ancient temple culture contrasted with sobering reminders of its recent past. Probably the most popular destination for tourists of Cambodia is the Angkor Wat Temple Complex.
Vietnam
Vietnam is a rapidly developing but still beautiful country that echoes its French colonial past (Hanoi) side by side with its Communist legacy (Saigon).
Places A Little Further Away...
Singapore is also within a 2-3 hour direct flight distance from other ASEAN countries, including Laos, Myanmar, Philippines, Burma and Brunei.
Also worth visiting, but a little further (up to 4-5 hours) include the Maldives Islands, Sri Lanka, India and Bangladesh, Western Australia (e.g. Perth), South China, Taiwan and Hong Kong and Macau.
Suggested Travel Websites
For any further information, the following travel sites may be useful, since they specialize in travel and information for the area around Singapore.
http://www.singaporehotelandtravel.com
http://www.asiatravel.com
http://www.lonelyplanet.com
For tickets and hotel bookings, the following site is recommended (similar to Expedia or Travelocity): http://www.zuji.com.sg
Recent wave on budget travelling has the following budget carriers: