For a few days it is as much about what you avoid as much as what you take in.
I'll miss some but first shot ...
Tiong Bahru, LPS, Orchid Garden, Chinese Garden, China Town with Food Centea, Asian Heritage Museum, Peranakan Museum, Baba House, Arab area, perhaps the Zoo, some named and specific hawker center and food courts, an evening walk but no eating at Clarkes Quay, an evening walk around Fullerton for the light show and atmosphere ...
EDITED: I'd like to see some better guides and maps as to how extensive and joined up are the air-conditioned underground walkways are. They are much more connected and extensive than most visitors will know or find out about.
On questioning perhaps Orchard, perhaps the Birds and less so Sentosa. I don't get Sentosa at all, and feel much the same about Gardens by The Bay but understand that visitors should probably see them.
Does this make me a bad person?
If you're going to Chinatown and are going to be close to the Maxwell hawker place then you really ought to check out the URA's Singapore City Gallery:
http://www.ura.gov.sg/uol/citygallery
This is well worth seeing and gives you much more perspective on how big (or small depending on your pov) Singapore is, how it's spaced out, a view into the various parts of the city, not to mention a very detailed view of the core (central) area and in which direction everything is heading (you'll see what's planned but hasn't been built yet).
If you check out the MRT map you'll see a "Downtown" station which is a slightly chilling thought considering there is not much there yet.