They have bus tour of Singapore; it takes about 2 hours. Go to the Singapore Visitors Centre bureau in Changai for tickets. If you want to do it on your own you can get the metro in (1 change of line required) or the public bus. Singapore’s such a great place that if you can change your flights it would be well worth it to stay for a few nights on your way back. But there’s a load to do in the airport to keep you occupied for 6 hours. There’s a place you can take showers and chill out (the Oasis lounge?), free internet, a pool with carp, massage chairs, a cinema, a roof garden with sunflowers, shops, restos and bars. [That being said, I ordered a Singapore Sling, which turned out to be pre-made so they just added lemonade to some sort of mix in a plastic container, in the bar upstairs beside the cinema and got such an allergic reaction from whatever they had it. I was so sick that they almost didn’t let me on my flight home].