Having lived in Singapore for 12 years, here is what I have to offer in terms of my favorite local food.
Best non-East Coast seafood, on the corner of Aljunied and Geylang Road, open air tables line the shops after they close along Geylang Road. The place gets real packed on weekend nights and the food is very reasonably priced. We had dinner for 4 once and ordered lobster salad, kangkung belachan, black pepper crab, chili crab, crayfish, fried rice, drunken prawn and some desert and it was only $130 Sing dollars, a real bargain!
2 Late Night Eats!
East Coast Road after you past Siglap Center, you will see a 24 hour Malay coffee shop. They have the best mee goreng, wrapped in egg, omelete style, when you order it and you break the egg open, the piping hot noodles is there for your enjoyment all at a cost of $3.
Somewhere in Bedok

in one of the HDB complex lies a 24 hour noodle shop that serves minced pork noodles. Went there at 2am one day and had to wait 20 mins before my order was served to our tables. They offer $2, ,$3 and $4 sizes, take my advice, order the $4 bowl you will not regret it.
That's all. I have not been home for 2 years now so I have to really catch up the next time I go there!