as a singaporean here are my recommendations =)

about the hawker centers.. newton and lau pa sat aren't actually remarkable quality-wise, they're just the more tourist-oriented and expensive ones. if you are, for some reason, in the suburbs, the hawker centers there are just as good if not better, and more in tune with the singaporean lifestyle.

fine dining wise, there are a few places that i would say are fabulous but might not be really new or exceptional for you guys who are possibly used to these cuisines. i'm a singaporean college student with limited exposure to authentic french cuisine, for example, so im not a good judge =)

french: au jardin les amis, within the botanical gardens, has won zillions of awards and the setting is fabulous.
japanese: nadaman, at the shangri-la hotel
chinese: many! lei garden, li bai, club chinois (fusion chinese), tung lok (sharks fin) etc.
indian: i'm told rang mahal at the pan pacific is really awesome.
others: shrooms at chijmes, indochine in china square, lemongrass at the heeren shops, mezza9 at the crowne plaza, intermezzo at one raffles link etc are all great either from personal experience or from word-of-mouth.

enjoy