As you said, your problem will be the size of Texas... just driving from area to area can be most of a day in the car.
San Antonio is a must for a first time in Texas. Alamo is great if you can forgive some of the tourists (and a number of historic other missions if you're into that type of thing, they are much more contemplative), while the Riverwalk can be very romantic.
I'm not too wild about Austin, but if you're into live music in a bar, it can be great. NW of San Antone, or SW of Austin is the hill country, very nice natural area. Of course, it is impressive for Texans but may not be for Montanans

. Seems to me all the towns are very touristy, but you can find nice restaurants and such, and natural areas. There is one glass-blowing place outside Wimberly that I need to get back to. For water fun you can tube the river in New Braunfels, just a lazy day floating down the river...
I haven't been down to the border much myself. Lots and lots of open land, not sure how nice it would be. Big Bend NP is very nice but a heckuva long way. Some nice old towns in Big Bend area too, not sure about the rest of the border. With some altitude in the mountains the heat may not be too bad. Note it is almost equal distance from El Paso to Los Angeles as it is from El Paso to Houston... 600 miles from Big Bend to Corpus Christi. If you're going to Big Bend it's almost better to tour New Mexico and then go down to Big Bend.
Coast is nice too, Corpus Christi or South Padre Island. Not to much to do in Houston or Dallas IMHO (and I live in Dallas). Most areas not too bad on crime if you keep alert and don't play the target. Haven't been out Panhandle-way, but it's a damn big flat place. Kansas without the wheat?
Gun stuff:
Long guns OK in vehicles, loaded, wherever you want. Do keep it out of sight or someone will bust your window for it. Montana and Texas have CHL reciprocity for pistols, can't remember you saying if you had a Montana permit or not. Otherwise, no pistols in the passenger compartment! Unloaded & locked in trunk. With the CHL here they have cracked down on no-CHL pistols in vehicles (except RVs). National parks will have their own Federal rules, not sure about that. CHL carry in state parks is ok! Not sure about long guns in state parks, may need to be locked up so no chance of mistaking for a poacher. Let me know if you need more info on this, and TX carry in general.
I would not be on the border without a weapon either, strange stuff these days. Note Big Bend is a national park (but I'm sure lots of folks carry anywhays) but there is a state park next door, not sure of the name. I would like to do the float trip down the Rio Grande (if it has water), but a couple folks doing that got sniped from Mexico a decade ago or so...
Other thing is make sure your vehicle is in good condition with adequate spares and survival gear. Think hot and lonely and no cel coverage.