Mileage Lover,

Hilton isn't close to any hawker centre. By close, I mean walking distance. Newton doesn't count

Now, if we stretch it a little bit and game for a bus ride of 10 minutes and some walking (or a cab ride), there are some options. Bear in mind though, that the minute you step into a hawker centre, you'd stick out like a sore thumb because its mainly the locals that patronise it. You can refer to uk1's informative thread on how to choose a hawker stall.

Off the top of my head - nearby enough for you:
(1) Zion Road hawker centre, opposite Great World City - smallish hawker centre
(2) Tiong Bahru hawker centre, maybe 3 to 4 blocks from Zion Road hawker centre. Now, this is a large enough one that will give you a flavour of the offerings. Food that you may not be familiar with
(3) Empress Road market
(4) Hong Lim hawker centre at Chinatown, huge hawker centre gets crowded at especially at lunch
(5) Smith Street hawker centre at Chinatown huge hawker centre

Happy eating!