If you're going to go straight to the Night Safari/Zoo from the airport, do not take the MRT/bus unless you don't mind spending 2 hours on public transport..... Besides, you should be taking a taxi from Kranji station, not AMK. The zoo/safari is only 5-10 minutes away from Kranji.

Since you are flying SQ, do make sure that you get a Splendour card from the flight attendant on the plane, or find out where to collect one in the airport (using your boarding pass). The card gives you about 20% off all the major tourist sights, which is a good amount of savings.

The SIA hop-on bus may only run till early evening, and isn't very very frequent so when your time is limited, it is prob not a good option.

Other places to see:

1/ Orchid Garden at Botanical Gdns
2/ Jurong Bird Park
3/ Underwater world at Sentosa island
4/ Little India
5/ Haw Par Villa