Stayed a couple of years in Sinky before moving up north.
Here's a few picks of mine, not really tailored to the B3D crowd but might be worth a look or two:
Tiong Bahru. Small, quaint neighborhood with unique (in SG) low-rise housing. The food court in the local market is a great sampler for Singaporean food. Open Door Policy serves fantastic western fare, on the same lane as BooksActually, an interesting bookstore with a focus towards literature. Rather close by is Zouk, Singapore's premier douchebag club.
re: Hawker food, skip Lau Pat Sat and go for Maxwell food court in the city- near Tanjong Pagar station.
Asian Civilizations Museum. Pretty much the only cultural site you'd want to visit in SG; everything else is kinda westward pandering and banal (Art Museum, 8Q, Art-Science Museum).
The National Gallery opens in October so it might be worth checking out if anything for the architecture, which is built into the old Supreme Court and City Hall buildings.
Skip the Singapore Flyer and head for Gardens by the Bay. IMHO the view from the OCBC Skyway is much nicer than on the Flyer. The 2 conservatories are worth visiting for their funky layout, architecture, and robust air-conditioning (lol) too.
Tanjong Beach Club. Really nice beach bar on Sentosa Island, picturesque enough to make you forget why you're doing this in SIN for 3x the price instead of Bali or Phuket. But to unwind on a sunny day it's good.
Boon Tong Kee Chicken rice. Don't leave Singapore without having this. Beats anything you'll have in Malaysia- nay, Melaka. As an ex-Malaccan, I'm pretty confident