The Remington Restaurant at St. Regis Houston I'm not much of a meat eater but every time I stay at Houston's St. Regis I have to order the St. Regis burger. I don't know what they do to it but it is the moistest, most satisfying burger I've ever had. I've had it both in the restaurant and room service, but it's usually room service.
Also, Le Meridien Cancun has a sandwich that I order out by the pool(Le St. Trop is the restaurant) that is mouth-watering. It's a Chicken Ciabatta and I was there last month and they didn't have it on the menu. BUT, they made it for me anyway. Chicken, a light cheese, and a huge grilled portobello mushroom w/ grilled onions- it is worth the stay just to get the sandwich.
"Ailoili" (Their main restaurant) is very nice and has a wonderful breakfast buffet- the amazing array of bread/rolls is spectacular. It's like going to a bakery. It's definitely worth the exercise you need to do later.
I'm a room service junkie but it is nice when you find a restaurant you like at a hotel you frequent. In fact, I believe that these special favorites are a huge part of why I return to these 2 hotels again and again.