Nothing wrong with I-10 thru Houston now that the construction on the W. side of town is finished, just go thru in off peak hrs. Get in the center land and don't get out of it.
We have good friends just out of Fredericksburg and go there at least yearly. That's really pretty country, good people, food and lots to do and see.
The option of Tx. 105 thru Conroe is good, we've taken it several times. The big drawback is it puts you on US290 which runs thru Austin, as bad or worse than Houston was.
Best bet is pick out a town that you want to use as a homebase and work out from there. Most everything will be within a +-70mi. radius. I would pick Fredericksburg, Kerrville or Marble Falls. Just get on some of the Fm. roads and follow your nose, very few dead ends in that part of the country.
Enjoy your trip. Warning though, the Hill Country can be addictive.
Dave, Miss Sue and Lucy the Scotty
00 Windsor, 40', Grand Cherokee Limited