Second the night zoo, amazing experience, make sure you do some of the walking trail in there too not just the bus.
Taxis are cheap, if there are two of you it works out similar to the bus, if there are three of you a taxi is cheaper.
I liked China Town much more than Little India. If you like urban stuff the kids ride BMX and skateboards in some of the underground linkways between the shops, but it is 100% safe everywhere.
Got to go to Raffles and have a Singapore Sling, even if you are not a drinker, and the peanut shells on the floor as well as all the stuff with history in there make for a very atmospheric place. Some of the high rise bars give spectacular views over the city at night.
The Merlion is weird! But the walk around the waterfront very nice, good restaurants, great photo ops, etc. Awesome aquarium at Sentoza too.
The place is not a closed in, tight, type city, it is the kind of place where a 24mm can work better than a 16mm, if you understand wheat I mean. There is space, it isn't Hong Kong or Delhi!