I ditto the idea of staying closer to downtown. There are a ton of hotels to choose from -- Hampton Suites to the Driskill. It's not worth dealing with the rush hour traffic and being far from the action.
On the way to Houston, stop to take a tour of the Blue Bell ice cream factory in Brenham, just off of 290. The late great RW Apple of the NYT rhapsodied about Blue Bell's ice cream, especially the pecan praline. Definitely a local favorite.
http://www.bluebell.com/
Just this week had a pleasant surprise in the Warehouse District by eating at the Capitol Brasserie. Very good French bistro food. Malaga is another favorite in the Warehouse District. Chez Nous near Esther's Follies seems to have come back after losing its chef a few years ago.
We eat out way too much for work. Our favorite restaurant is Uchi. Other upscale favorites are Jeffrey's, Hudson's on the Bend and Vespaio. Shoreline Grill was a favorite for work until they raised the prices. But the Shoreline Grill is bat-adjacent, so that counts for something.
While I am not a big fan of Fredericksburg per se (after one or two cutsey shops, you're done), I love the area for bike-riding and wine-tasting. Also, my parents always love to tour the LBJ birthplace and ranch. (Love LBJ's prize-winning herd!) You might want to think about staying in the area after visiting the Nimitz Museum. That way you will not be so rushed to get to Austin. There are a lot of nice B&Bs in the area. Also, if you will be there this spring, the wildflowers are starting to look great.
If you are literary types there is a ton to do here, also. Perry Mason, anyone? (or O Henry...)