For dude ranch possibilities, go to www.duderanches.com, click on Texas and you will see many possibilities for places close to San Antonio and Austin.
Austin has a great live music and restaurant scene. There is a very active food truck scene as well. Be aware that the University of Texas at Austin Longhorns have home football games on Sept. 1 and 8 and Oct. 6 and 20. The University's Family Weekend is scheduled for Oct. 26-28. All of these events will impact hotel availabililty and price, so plan accordingly and reserve early if your itinerary takes you to Austin on any of these weekends.
Check out the Spanish Missions in San Antonio. There are five, one of which is the Alamo which is right downtown. The other four are close by, but not downtown. Seeing them is a great way to get a feel for the influence of the Mexican culture on this part of Texas.
I agree with knr--if you can get to West Texas Big Bend National Park is spectacular. There is only one place to stay within the park (unless you camp) which is called Chisos Mountains Lodge. It books quickly, so if you are interested book sooner rather than later. Make sure you book through Forever Resorts which is the vendor which runs the lodge. Don't go through a third party, even if their name is national park reservations or some such thing. It takes about 7 hours drive there from San Antonio; about 8.5 hours or a bit more from there to Austin. Unless you want to do some serious hiking a couple of nights there would work.
As far as itinerary, you could fly into Houston, do your coastal thing, drive to San Antonio, on to Big Bend (if you choose), drive back to Austin and then back to Houston for the trip home.You could also reverse the order, of course.