If nobody has told you yet, singaporeans have 3 main passions: food, shopping, and food!
Having travelled all through asia, I'd have to say Singapore is the "safest" place for you to try asian food, we've got great local food (i.e. chinese, malaysian, indonesian and indian) as well as western cuisine, and it's not just in pricey hotel/boutique restaurants either. Singaporeans delight in going one place for dinner, another place for desert, and yet another place for coffee/tea, thus "showing casing" their knowledge of the best places for the appropriate courses.
Kinokuniya is a definite visit; borders and barnes& noble are just no comparison for sheer variety.
I also find electronics are quite reasonably priced compared to Europe and Americas, Sim Lim Square is the place to go for parts, with Funan Centre as a more upmarket consumer place. For cameras, highly recommend Alan Photo in Sim Lim (ground floor - although in Singapore we'd call it the first floor; no ground floor in singapore) - not sure if the Alan Photo at Funan is related.
Tailoring wise please see the thread that My View2 has highlighted already.
Hope this helps.