driving to the city centre will take aboout 30mins, so you can probably drive through using the East highway and see the Marina area heading towards Orchard Shopping district to the Chinatown Area then towards Little India and take the Central Higway to see the bird houses on your way back to airport.
The security and immigration lines takes less than 10mins.
Changi Airport has an outdoor swimming pool if you dont want to stay inside the airport and do all the rush driving around.