Singapore airport is great, and really geared to the transit traveller.

As others have said plenty to do at the airport if you wish to stay there, pool, day hotel, even a spa if you fancy.
But if you want to go into the city, before you leave immigration, go to the Singapore Tourist desk, they offer several tours into the city, complimentary. They offer a 4hr, 6hr, and 8hr tour I think, whatever fits your schedule, and they guarantee to get you back airside again with plenty of time. If you don't fancy any of their tours, you can also get a metro pass from them (free), and go do your own thing. If you've never been before, would recommend the tour, and get an idea for the city.

We always have a 9 hour plus break in Singapore, watch a film at the free cinema and grab a massage. Short sleep, shower and something to eat, helps you tackle the next leg of the flight!!!

Bromsgrove, not far from where we used to live!