Keep in mind, Houston is ~3 hours in a car from Austin (2 and a half if you stay on the far west side) and that is without traffic. There are two basic direct routes from Houston to Austin, and one goes right by the Austin airport (KAUS)... That route will be HORRIBLE traffic-wise, I'd assume (since, you know, airport, and the track is near the airport, and...). They're not letting people drive themselves to the track, either, so you'll have to go to one of the pick-up points. If they make one out down 71 (east of Austin), that'll be perfect. You can skip the city traffic and just go I-10 to 71 and get there. But if not, you either get to go the north route up to 290, or stay on I-10 longer and come up somewhere. Unfortunately, US 183 (which is suggested by Google Maps) will not be a good place to come up - it goes rather close to the airport and will also have nasty traffic.
Alternatively, you can come to H2R, which should avoid most of the bad traffic (I-10 westbound and then San Marcos Freeway aka TX 80). You can then take a western route into Austin, which should be lighter traffic.
BTW, if any of my road-talk sounds confusing, I'll be happy to share routes on google maps or whatever.
Both San Antonio and Houston have lots to do, with recommendations varying by your interests and budget. Houston has a huge number of museums, both have lots of parks and Texas history, San Antonio has more theme parks (bigger budget needed), Houston has Hennessey. Also, about an hour south of Houston is Galveston. This will let you see the Texas beaches (which are sandy, but the water is murky, not great beaches) and is a good place to see some more Texas history and understand the impact hurricanes can have. Galveston also has Moody Gardens, which has a nice aquarium and a wonderful "Rainforest Pyramid". In the rainforest pyramid, you wander on a path among the trees, plants, and streams... as birds, mammals, etc wander freely with you. While there are a few cages, few of the animals are actually caged. When my mother and I went there, we ended up being inches away from a parrot, a
Victoria Crowned Pigeon, some monkeys, and some bats. Moody Gardens is on the expensive side.
San Antonio has the Alamo, the
Riverwalk, a Sea World,
Six Flags Fiesta Texas, and various other things. Unfortunately, the current schedule shows Six Flags as closed except for weekends. They may realize F1 brings in a lot of people and open up some weekdays, they may not. Sea World looks to be open the week after F1 (which is Thanksgiving week, here in the US). But San Antonio has its share of museums and other activities, as well.
Beyond that, there's also various small towns in the area and the Hill Country, which is to the west/northwest of San Antonio/Houston. It's great for driving, and has some state parks and the like.
So... what kind of stuff interests people?