Pummel, I lived in that region for almost 15 years including 7 years in Singapore and 5 in Philippines it's a brilliant place to live but in all honestly not that great for GA. As ETOPS said there's not much in the way of light aviation in Singapore. For a tiny island that has three active airbases and a major airport airspace is pretty crowded to say the least. I do recall that Singapore Airlines operated a couple of Pipers ( Cherokee or Arrow not sure) but I don't know if they were available to Joe public. Last I heard Seletar was being set up as a bizjet servicing hub , so there might be some other opportunities there, it's a few years since I left.
Malaysia is your best best. there's a few private strips such as Segamat where they skydive and fly.
Philippines and Thailand are much better for GA and there are more places to see and go, but that may not be helpful if you're going to be located in Singapore.
I ended up taking up skydiving just to get airborne when I was living in Singapore which probably shows how desperate the situation was !