t's hard to pick a top 3, since different people have different interests.
In general I would have to say:
Sentosa Island, Zoo, and the Merlion fountain (at the harbor)
However for the gardener the Botanic Garden is a must see. The garden is 52 hectares and isn't your normal garden! There you will find a second garden, the Orchid garden, jogging paths, picnic areas, natural wooded area, open manicured area for playing games, a restaurant, and of course a gift shop. I was very surprised to find that not only bus loads of tourists, but just as many locals having fun. Because of its size it never felt crowed. Best of all it's FREE!! The only area that charges it the Orchid and it was only a couple of dollars.
For the animal lover, one must do the killer four, zoo, night safari, Jurong bird park and the butterfly park. This is a full day of fun. The zoo is one of the top rated in the world!
For the shopper, you have Orchid Rd for high end, Chinatown for the bargains, and Arab street and little India to round things out.
Then of course there is the Ruffles Hotel. Even if people don't stay there, they stop by to photograph the doorman.
While there are many websites on Singapore, I found this one to offer a lot of info. and is the one I used the most before I went.