3 days in SIN is enough. Do 2-3 days in SIN, go elsewhere for 2-3 days, return to SIN to complete your journey.

Stick with SQ, Silkair (SQ subsidiary), Jetstar or Tiger. Look on zuji.com for deals. Look on Amex pay-with-point MR site fror resort deals.

For ease with low probability of visa difficulties - Thailand (Bangkok or any of the many beach/island resort areas) or Bali. Worth investigating visa issues - Vietnam (Hanoi or Halong Bay) or Cambodia (Siem Reap/Angkor Wat).

If you go to Siem Reap (I highly recommend BTW) I suggest you not scrimp on accomodations. The very attractively priced local places can be serviceable but a bit rough. Depends on how "comfortable" you need to be.

If you are willing to go farther afield for a once-in-a-lifetime experience, get a PRC visa and go to Chengdu. SQ does direct flights and you can visit the Panda Research Center to hold a panda in your lap (for 1000RMB!)