Texas is as rich in history and as scenically diversified , as it is big.
I hope your vacation begins not in San Antonio but as soon as you get to Texas, I've lived all over the world (England included) and some of my greatest memories are from Galveston. Also, I think you'll find that Texas is burgeoning with so much charm -if you're into rustic, that even for a beach town Galveston is old-timey and certainly unique.
If you're looking for pharmacies that still double as shake shops and real salon towns that aren't tourist sites, or even pit stops where people speak Texas German to this day (Fredricksburg, Luckenbach) then Texas is the spot. Hill Country is a big part of the state, I recommend Marble Falls.
And don't forget all the natural hot springs!
Traveling around the Big Bend, and boy are you in for a mind blowing experience, you'll find little Mexican boarder towns (the Jalapeno's will knock your socks off), and even tiny islands you can reach by paddle boats for hire, where you'll end up in the local restaurant which also happens to be someone's kitchen.
Big Bend has a lot of different facets from basins to peaks, a river rafting trip alone takes a whole day. You'll need a minimum of 4 days to even get a scope of it.
Good call on Marfa and Alpine, if rural is what you wanted then that's what you're going to get around there.
You'll see more sand dunes and road runners than you will people, once you find a town with an antique store and a train track you've hit civilization.
I wouldn't overlook the South East, you could spend three weeks in that area alone.
I think you would much prefer Padre Island to Corpus Christie, one's virtually untouched the other is a pretty well trafficked beach city.
The Texas Almanac will be indispensable for this trip.