I would definitely avoid Lau Pa Sat --- food quality is awful. Office workers only buy food here because it's convenient to the CBD.
If you do stay at the Conrad, there is a far better (though admittedly more expensive) hawker centre called Gluttons Bay. It is also for tourists, but the food quality is far superior to Lau Pa Sat.
For a different food experience you could try Peranakan (the cuisine from Malay-Chinese families) --- the best is probably Blue Ginger, but it is pricey. Good Peranakan food is hard to find these days.