If your sole objective in leaving the transit area is to get air, there are plenty of outdoor terraces within SIN's sterile area, well-designed for relaxation. I believe they even have an outdoor pool.

Also, there is really nowhere to go outside the airport within walking distance. If you decided to take a cab, well-- the only place worth visiting at that time of night would be downtown. If you decide to do that, you should try to keep your own taxi, since one of the few black marks on Singapore's reputation for efficiency is the availability of taxis (or lack thereof).