Singapore Air runs a "Hop On Hop Off" bus around the city that hits many major sights. Riding the bus is a good basic tour and you can exit the bus at each place you want to visit.

Mandai Orchid Gardens are beautiful and would be a good choice if you don't have the time to see the more distant gardens.

I think Sentosa is overrated and kind of boring.

You can make a reservation for breakfast or afternoon tea at the Zoo, your companion will be one of their orangutans. The Night Safari is the only nocturnal zoo in the world.

The afternoon tea at Raffles Hotel is very nice, as previously mentioned a drink at the Raffles Long Bar is fun (touristy, but almost a must).

If you are interested in WW2 history, the "Battle Box" dioramas and dramatization are located it Ft. Canning Park. You walk through the large underground bunker system, HQ of the British during the fall of Singapore in 1942.