Lived there for a couple of years in the mid-90's.
If you have been a week you have probably seen most of the island, but some things to do:
-Sentosa Island
-Singapore slings and peanuts on the floor at the Raffles hotel
-Eat at any (and all) hawker stalls you find (you will miss those)
-Teh Tarik (I still miss those)
-Some shopping at Takashimaya or anywhere in Orchard Road
-Chili crab at East Coast Parkway
-A trip to Johor Bahru
-Read 'No money, no honey' by David Brazil on your way back to find out what you have missed
Too many things to do in just one weekend. Enjoy-lah!!