A few things:

1)Definitely take a taxi into town. It's very easy and from a U.S. perspective, a relatively good bargin.

2) If you aren't tired when you arrive, after you check into your hotel, wander (or take a taxi) depending on how far you are) over to Boat Quay along the river. Walk around and soak up the feel of a Singapore night. Then walk a few blocks to the outdoor 24 hour food emporium called Lau Pa Sat. The food is awesome and really cheap. It's also a relatively clean environment. I've said it before and I'll say it again: The food in Singapore is probably the best I've had anywhere that I've been to in the world.

3) Go to the Night Safari. I'm not much of a zoo person (I don't care for the whole idea of confining animals to cages -- but I do like to eat them -- that's another issue). But this is really unlike other zoos because you get to see animals in habitats that seem to approximate their actual habitats and you get to see them at night -- when they're awake and not sitting on their a*ses. The bat cage is particularly cool -- it helped me overcome my fear of bats.

4) Take a taxi just for a tour. During my last trip to SIN, four of us -- Kenji, Highflyah, Iluv2fly and myself -- took a taxi and had him just show us around the city. The rate was incredibly reasonable. He was really honest and also a pretty good tour guide. We spent maybe 2 hours and I got to see parts of the city I had never been before -- like the last remaining remnants of the old Chinatown. He did take us to a cheesy rock/gem store at the end -- where he probably gets a fee for bringing us. But we didn't buy anything and just looked around.

5) Do a search in Trip Reports, Mileage Runs and United under my name and you'll see some of my and others' comments regarding what to do in Singapore. Have fun!!