So, spoke to the wife about it, and she definitely wants a road trip. Coming from Australia, I have no issues with driving 8 hours or more if there's something worth seeing.
Basically, I'd like to see "real" Texas, or as close as possible. My theory is that cities are all basically interchangeable since the internet, so I'd rather see interesting small towns, and natural beauty.
On the general wish list though, is good barbecue, hopefully some country music (I'm interested in the western swing/bluegrass/outlaw side of things, not what passes for country music these days), a few hikes in nature, and maybe some art galleries/museums in Austin (because we'll stay one night there), unless one of the other cities is a better place to go. I haven't really heard anything positive about Dallas or Houston, but they might worthwhile.
If there's something that I "must" see or do to get a proper Texas experience, let me know, it's pretty much open at this stage.
Small towns in the Texas triangle: Fredericksburg (touristy "old town", west of Austin), Castroville (west of Austin) is good, too, got a great bakery and there's a meat market that sells this one specialty item made of lime juice-cured raw beef, processed cheese, and onions, New Braunfels is another fun place to check out, seasonally there's a river you can tube down, and another "old town" area...
Nature areas: lots of forests north of Houston (you can do research into the various trailheads and parks), a few parks around Austin. Lost Pines State Park was good but most of the forest burned down about a decade ago and it's not the same.
Austin area: Fredericksburg is fun, it's west of Austin. It's near Enchanted Rock but it's sadly pretty busy these days. However, near Houston there's large forests to the north with lots of trailheads and a few parks.
Waco is a bit of an oddball because it's not really a small town but not a big one either. Would recommend the Dr Pepper Museum downtown but parking isn't free anymore.
Houston has some museums in the appropriately-named Museum District and an interesting "Chinatown" strip...San Antonio has the Riverwalk...
Barbecue is going to be hit and miss, beef prices means they're not cheap like they used to be, and every city is going to have what they consider to be the "best". Lockhart is supposed to be the "barbecue capital of the world" but the only ones I've tried are kind of mediocre.
There's a chain called Rudy's that can be found just about anywhere and people will sneer at you for it, but it's at least consistent, decent, a fun experience (the restaurants are just big galleries with covered picnic tables and paper towels instead of napkins) and won't pull stunts like "run out of meat for the day".
There's also another chain called Buc-ee's, which is a giant gas/convenience store chain that has made-to-order foods, large clean restrooms, and knick-knacks. Visit at least one. They have billboards everywhere.