Assuming you'll be coming out I-10 and then picking up SR71 towards Austin, there's also quite a lot to pick from in the Bastrop area which is about 30 miles east of Austin. These places are more budget friendly than the Fredericksburg area.
A new place just opened in Kemah, off I-10...nice, but very close to 10.
https://summerbreezeusa.com/
Whatever you do, don't make your trip at night. The construction activity along I-10, west of Houston goes on for a good 20-30 miles from Katy. There are multiple lane closures at night which make traffic horrendous.