Lots of very good places near the Palmer House Hilton...
Vivere (Italian - part of the Italian Village complex - Vivere is great, but I don't recommend the other parts there)
Trattoria No. 10 (Italian)
Atwood Cafe (upscale American, and also open for breakfast)
Park Grill (contemporary American)
Pizano's (Chicago deep-dish pizza)
All of these are within a block or two of the Palmer House. There are plenty more excellent places 5-10 blocks away, but these are the closest really good places.
I've used the restaurant.com coupons. They work. Although, like the Entertainment book, a lot of them are for places you wouldn't necessarily want to go to. But it's worth checking to see if they have them for anyplace you're already considering.
For a casual French place for lunch, not too expensive, I can't think of anything really close to the Palmer House Hilton, but about a mile away,
Bistro 110 and
Kiki's Bistro are both pretty good.