If you want to try a local pizza joint that's been around forever and is pretty good, try Big Ed's near University Dr and 231/431. Pane e Vino as others have stated is very close to your hotel, very good pizza as well (same owner as Cotton Row and Commerce Kitchen below)
Connors has the best steak (the dry aged prime) in town, hands down, I've eaten there half a dozen or more times and it has been amazing every time. Beats the heck out of Ruth any day.
The Brazilian steakhouse is good as well, but not as big as a Fogo de Chao or as many meat choices, they had 15 different cuts if I recall correctly.
Near walking distance to your hotel a very good restaurant is Cotton Row, a less "upscale" version of Cotton Row is at the opposite end of the building called Commerce Kitchen, they are both very good.
If you are into craft beers, within half a mile of your hotel is Below the Radar, and less than 3 miles away is Huntsville Brewery (on 801 Franklin Street), both have a massive number of taps of a lot of local beers (Huntsville Brewery has a lot more taps).
Best TX style BBQ is at ChuckWagon BBQ out near the Huntsville Airport. They have absolutely the best brisket, ribs, and chicken in town.