A few things to add here, although I generally support most of the recommendations.
Breakfast/Brunch - if you aren't opposed to heading into the heights, Down House offers one of the finest combined cocktail/food programs that can be had before noon. Hugo's would be my first choice for an iconic Houston brunch, but it's also buffet-style, which isn't my first choice. Honeymoon appears to be a similar option to Down House that is closer to your hotel, but I've only had the cocktails there and can't vouch for the food. Hearsay has never been a favorite of mine, and I would opt for Batanga (across the street) if forced to choose between the two, particularly if it happens to be on a Sunday when all the bottles of wine are half-priced. Another market square area option is El Big Bad. The fish tacos are good, but I haven't had much else. House-infused tequilas and creative margarita options are the primary appeal there.
Neil T's dinner recommendations are pretty on point. I'd nix Reef though and add in Coltivare and Pax as suggested and consider Liberty Kitchen River Oaks, Holley's, Goode Co. Seafood, or Prego if you were in the mood for a really good seafood dinner at a spot other than Reef. Oxheart is my favorite restaurant in town, but you may not be able to get a reservation at this point.
If you're in the mood for fine craft beer selection/ice house feel but don't want to compromise on food offerings, consider D&T ice house or Moon Tower Inn, although the latter lacks TVs and ambience. Mongoose vs. Cobra has limited food but also great beer/drinks.
Since so many solid suggestions have been made, the only other dinner option that I will throw out there is Roost. It's a little more casual, but the food is top notch and reflects the diversity of the Houston restaurant scene on one menu, much like Underbelly.
Lastly, Backstreet Café is a great spot for brunch, lunch or dinner - charming atmosphere, a large, well-executed menu with something for everyone, and a solid drink program. Coincidentally, it is owned and operated by the same group that runs Hugo's (and Prego and Caracol).
ETA: my commentary really only focuses on downtown options or spots that are a short cab/uber away.
