the public transport system (underground & buses) is excellent so you can get around very easily. the night zoo is an unusual but very interesting place with all the nocturnal animals active. if you want a good alfresco meal try newton circus where there are loads of open air stalls selling all kinds of quality food. choose your stall, order your food, grab a table & wait to be served.
you shouldn't leave without a visit to raffles hotel. although they're not cheap you should try a singapore sling there (that's where they were first created). the tradition is to accompany your drink with complimentary monkey nuts & throw the shells on the floor. you'll find yourself ankle deep in them before long.
wear your city shirt at all times & give grief to any plastic rags you see there. are you going in the near future or later this year? if you're going soon take an umbrella as it's the wet season & it's pissing down.