As I said in a previous blog post about Singapore Budget tips, one of the best ways to experience Singapore's food scene is to eat in various hawker centers. Unfortunately, I wasn't able to shoot a video for it [too busy eating], I just happened upon a video which best explains the variety of food and culture you can have in one place.
Personally, I've been to Chinatown Food Center, Albert Food Center [in Bugis], the Tekka Food Market and Bersih Food Center [in Little India] and ate some carrot cake outside the Ang Mo Kio MRT station. As you might imagine, these hawker stalls are visible from almost every MRT location in Singapore, so you can't miss it.
Friendly tip, don't get stuck in restaurants. Sweat it out, enjoy a little company when someone sits by your table during rush hour and eat hawker stall offerings. It's more than worth it.