i liked Sentosa island...lots to do there and you could spend the whole day there.
Also go to the Zoo - this place is cool. Its an 'open' zoo, much like Dubbo (assuming you know Dubbo Zoo). Even if you're not a Zoo fan, this is a different experience. Try the Night Safari, I didnt get a chance to, but have heard its really good.
If you want to go out for dinner, try Chjimes, its old church grounds and has been turned into lots of restaurants (mainly western) and shops and pubs. Very cool. If you want more local, traditional food there's a food market (hawker style) in Chinatown somewhere.
Anyway singapore is a great place, enjoy