Alex,
I've been a regular visitor to SIN for 10 years now and seen little General Aviation activity - looks like Seletar is where some light aircraft are allowed.
I use the word "allowed" on purpose as every facet of life there is tightly regulated by the government. The idea of large numbers of the citizens whizzing about in Pipers, Cessnas or RV-7s would simply not be countenanced.
Expect it to be reasonably difficult and quite expensive with more restrictions than the UK. If you can push through that then I would think some enjoyable trips - Malaysia etc - would be possible.
As an aside, when I first tried to play golf there I thought the course was run by escaped Gestapo officers!!
Good luck and take plenty of ID
