Singapore makes an excellent base to explore the region since it has what is often deemed the world's best airport and
is a hub for regional discount airlines, including Air Asia and Jetstar. These airlines generally do not appear in standard search engines like Orbitz but can be much cheaper. One-way flights are usually half of round-trip flights, so you can buy a string of one-ways from destination to destination, perhaps as far as the Philippines or Hong Kong or Nepal before returning back to Singapore. Singapore has great food and is lush and green with inexpensive taxis, probably as cheap or cheaper than public transport if two or more are traveling together. I would recommend the Singapore Zoo, one of the world's finest, and the neighboring Night Safari which is only open after dark — when the animals are most active, which is the point. Also recommended is the Jurong Bird Park, where you can see thousands of Asia's most colorful birds up close.
From Singapore, it's a short flight to Malaysian Borneo. Kuching is a beautiful city with an attractive riverwalk. Day tours can include an Orangutan Sanctuary, and the Sarawak Museum started by Darwin contemporary Alfred Russel Wallace. A day or overnight trip to Bako National Park is highly recommended; there are beach walks, boardwalks and forest walks and you will see bearded pigs, tiny crabs and mudskippers on the beach and monkeys galore. Sit in the food area and you may see them steal food and sodas from unwary customers! You can arrange a multi-day trip upriver to visit the longhouses of former headhunting tribes (with woven bags of skulls still on display). You can also arrange a overnight stay including a short flight in a tiny plane to Gunung Mulu National Park. Gunung Mulu has spiked granite pinnacles in a primary rainforest setting. There are long boardwalks through the rainforest, leading to a variety of caves, the largest of which has a cathedral-like ceiling where millions of bats sleep. Walking through the caves and through the rainforest, especially at night (some plants glow) is an otherworldly experience you won't encounter in many places on earth. Be prepared for leeches, though!
Angkor Wat is not to be missed; 4-star hotels can be booked through Agoda for $30-$40 a night including breakfast; tuk-tuks cost a dollar or two and a taxi can be hired for the day to take you from point to point quite inexpensively (the ruins are massive!). Thailand is not as cheap as it use to be, but the people are friendly, and the street food can generally be trusted and is cheap. Phuket offers the island experience. Bangkok is chaotic but is great for bargain shopping, either street markets or the MBK shopping mall which has many floors containing little independent shops, places to eat Western food like pizza when you begin to miss it, and fancy first-run movie theaters with $3-$4 ticket prices; American blockbusters are in English with Thai subtitles. Chiang Mai is the jumping off point for visiting the hill tribes and riding an elephant through the forest. Bali is also within easy reach; the local art and the Hindu flower offerings are interesting and distinctive; all-day taxis are inexpensive and can take you to local temples, rice fields and the Monkey Forest and will stop whenever and wherever you'd like. I seem to recall a reptile sanctuary where you can see the Komodo dragon, adjacent to a nice bird sanctuary.