It's been awhile, but I used to live there around 1997/1998. Does not sound like you'll have time, but the courses on the island were a bit limited, with the best clubs being private or semi-private. Also, rounds could often run 4:30 or 5:00, so you need to plan on that.
My favorite courses were a 45 minute high speed ferry ride away in Bintan (Indonesia). They had a great Nicklaus course and an excellent Norman course, along with 1 or 2 others, at the Banyan Tree resort on Bintan for example.
I also had a course that I really enjoyed, about 30 minutes north of Singapore in Malaysia, up what at the time, was the new toll road into Malaysia across the "second link" bridge on the west end of the island. There were a few public resort courses, I cannot remember the name of the one I used to play frequently, but it had 3 nines and was very nicely maintained and cut out of the Malaysian countryside. The only issue here is that it's sort of the other side of the island and then 30 minutes into Malaysia, so could be 1:15 or 1:20 travel time to the airport and wouldn't work if you only had a half day layover.
Jud's right, though, Blue Canyon in Phuket was always one of my favorite destinations. Check that out someday if you get the opportunity!