Thailand, of course, is an obvious option, strong tourist infrastructure, relatively cheap, plenty of stuff to do. And of course the food!
I'd recommend hitting the Philippines also, pretty cheap, english speaking, extremely friendly and easy to get around and not a whole lot of tourists, especially outside of Manila. Palawan has some beautiful resorts.
I also like Malaysia a whole lot, easy to get to from Singapore, fabulous food and an interesting culture. Panang is great as is Malaka. I've never been to Borneo but those who I know who have rave about it.
I'm off to India in June for a wedding so I've also been debating where elso to hit in Asia that I haven't been. Top of the list right now is Vietnam, although mostly because I'm on a vietnamese eating kick which I guess is as good a reason as any for picking a destination.