I was only in Singapore for one day and night but because it is such a well organized city I was able to see a lot of the city. I think the best way to see as much as you can in a short period of time is to buy a ticket for a hop on/hop off bus. You can take the whole bus loop around and then decide the second time around where you want to get off. I also recommend listening to the audio tour on the bus, they do a pretty good job at giving you a quick history of the buildings and sights you are passing by.
Singapore is a very modern and clean city, with most everything in English. During my five week long trip this was one of my last stops and it was a nice break to be back in a big city and not have to struggle to get around and find things for a day.
+ Visit Marina Bay Sands on the water: hotel, skypark roof and restaurant, shopping, eating, skating.
+ Gardens by the Bay
+ Art/Science Museum
+ Singapore Flyer
+ Orchard Road shopping
+ 1-Altitude rooftop bar at night (1 Raffles Pl.)
+ Clarke Quay, street of bars & restaurants on the water