SIN is one of the easiest airports to use. The immigration is very efficient and the taxi ride to most anywhere is about 20 minutes.
The lounge is nice but there's nothing to do there. Since you're coming in daytime, you might as well go eat/shop/tour.
- there are some interesting museums if you're into that, Asian Civlizations, art, etc.
- try food at a hawker centre, like Maxwell or Newton Circus. Taxi drivers know where they are.
- go shopping. Orchard Rd has lots of great malls, my faves are Ngee Ann City and Paragon but there are many others. Outside of Orchard are other interesting places like
Tanglin Village (art and other wares), Holland Village (housewares, other things), and
Vivo (largest mall in Singapore). You can spend days in Vivo alone. There's a good food centre (= hawker centre with aircon), cineplex, and the fun Japanese "100¥" store, Daiso.
- explore the unique areas like Little India and Chinatown. Lots of stuff to see, buy, and eat. Visit the
Mustafa Centre that sells everything and is open 24/7. It's a madhouse but fun.
I wouldn't go to the zoo - you can see those creatures at any zoo anywhere. I also would avoid touristy areas like Clarke Quay since there's really nothing to do there in the afternoon (there's a Hooters there which tells you all you really need to know).