If you want a taste of Singapore why not go to 1 of the seafood places on the East Coast Expressway which is on the airport side of the city. The Pepper crab is a Singapore specialty. You will get a view of the skyline from there! Or stay at the airport to eat - there is a food centre near a car park .Someone should be able to tell you exactly where it is but it is landside and like all food centres in Singapore is very good. Alt. go to Changi village which will mean you won't be at the mercy of rush hour traffic as it close to airport.
PS. Let us know what you eventually decide to do and how you get on.