May I suggest the following? Visit the Botanical Gardens (free admission) - plenty to see here including some amazing orchids. Then, get a taxi back to town (taxis are really inexpensive here) and get the driver to suggest a lunch venue off the tourist track. If you like seafood be sure to try the chilli-crab - a Singapore delicacy. A peep into Raffles is worth doing, but their Singapore Sling is not what it used to be. Personally I wouldn't waste time shopping, but duty free prices on cameras etc. are good.
Boat Quay and Clarke Quay are worth visiting particularly by night. Enjoy the trip!