You don't have to be a gardener to enjoy the Mandai Orchid Gardens. They're stunning:
http://www.mandai.com.sg/
The best way to see the harbour is by taking an evening boat trip.
As 3435anneh states, a visit to Raffle's Hotel is almost compulsory for tourists in Singapore. (Head for the Long Bar and order a Singapore Sling).
You can also take a coach tour over the causeway into Malaysia.
Chris
PS: Always check your change in hotel bars. It's illegal to give or receive tips in Singapore but bar staff seem to boost their income through the 'tips' that they receive when they 'accidentally forget' to give you your change.