Since you asked..
Try the food before you go to tour, Singapore has an interesting way of helping foreigners who stay in SG not be homesick, food from their home country. That way at least you won't feel moody while traveling.
Get lost, no kidding. Just not in the places you shouldn't. SG is small enough that.. you can be in Road A and somehow end up at Road E. Infact, one of the best ways to get around SG is by train.
Don't drink alot if you plan to ride the second world's largest ferris wheel(The Singapore Flyer)(Texas beat us by constructing one bigger). The ride is an hour long, and the toilet is only available on the first floor.
Oh did I mention F1 takes place in SG around this weekend.
As for places to visit, the Gardens by the Bay is a good place, admission tickets are cheap and you can always enter again for free on that day if you get the stamp at the exit. SG flyer as mentioned. Try the Duck Boat to get a once in a lifetime experience. Bring an umbrella, always. You are in a country just 1°N of the Equator, expect weather to be weird. Try to visit Pulau Ubin if you want one heck of a bicycle ride and the scenery. Head for Sentosa if you want a sort of amusement park experience.
Also a very very big tip, bring lots of cash. Stuff gets expensive for a country that depends on the tourism. And avoid saying anything negative, especially racial and social. If America is Freedom Singapore is Unity. Trust me, this multi racial country knows how to gang up on people if they start offending.