From a quick glance OK laws are complicated for out-of-staters, you probably need a stat issued LTC or some sort to be fully "legal."
Although most places in OK are very laid back.
Now, in Texas, you may see these signs where alcoholic beverages are sold:
Those are known as "blue" signs--as opposed to the "red" ones for "51%" venues. Those, technically, no longer apply to unlicensed carriers under our new 2021 permit-less carry law. Now, that does not mean that the people running the venue know that.
I know Arkansas just went to permit-less carry, but I do not know how that affects those from out of state. Perhaps our
@Spats McGee can weigh in on that.
Mentioned above are a number of fascinating places to visit here in Texas. Please note that Six Flags, Se World, and all the Schliterbahns (but not all water parks
per se et ley) are specifically "gun free." (For most of those the parking lots are a mess most of the time, and getting an Uber or Lyft to the venue is in your interest just for not having to search for parking in the Texas heat (and Summer is here--it's down to the 80s this w/e; but we're back to 90s next week).
You are likely to be on I-35 getting from DFW to Austin. You might want to stop in the town of West and get some kolaches ("koh Lah CHEE" a Czech pastry prized as a dessert or breakfast food*) About 40 minutes' later you'll hit Waco. Stop and visit the Texas Ranger Museum (east side of the highway just south of the Brazos River). There's a Fuego Grille in Waco just south of Baylor University, and it will have outstanding tacos.
Definitely take the Toll Road (130) when you get near Austin. If only to get a photo of the 85 MPH speed limit signs, but, mostly to get out of the Austin traffic as much as possible.
There's a very nice Best Western in Georgetown, if you have not chosen lodgings. But, if you want to be "near" downtown, there's a La Quinta at 12th & San Jacinto right off 35. It's 2 blocks from the Capitol and walking distance to Driskill Hotel, and 6th street. About 12-14 blocks south is the Congress Street bridge which has a colony of bats that come out at sunset. That used to be a touch sketchy for the "urban campers" preying upon the tourists, though.
Not quite an hour south of Austin is Gruene ("GREE nh") which is actually part of New Braunfels ("Noo brahn FELLS"--the locals call it "brawns fells"). This is perfect weather to hit up Rocking J and take a tube trip on the Guadalupe River. Or, to stop by the famous Gristmill for some classy chow. Gristmill is next door to Gruen Hall one of the oldest music venues in Texas.
San Antonio, as noted above is a unique place, and the traffic is a mess. The Downtown North Best Western is not a bad venue and is half the price of the BW on the Riverwalk. (The parking lot seems much nicer, too.) Uber can get you down to the Riverwalk. If you "do" downtown, definitely hit up historic Mi Tierra ("ME TEA er-ah") a Mexican restaurant that's near as lod as San Antonio. Afterwards, go to the bar at the historic Menger Hotel and get their mango ice cream to calm the spicy food down.
There's a rather nice gun range out in Helotes ("heh LOW tez") NW of San Antonio. Helotes is also home to Jon T Flore Coutry Store, yet another historic venue in the Texas music scene.
You will want to stop at Snow's in Lexington in your travel to or from, too. If you get there, early, on Saturday, they have smoked beef ribs. Probably a good idea to go to Texas Monthly's website and get the map for their Texas' Best Barbecue-- as you are talking about the core crown for BBQ in the state.
DFW to Austin is a stout four hours' drive (traffic permitting) down 35. San Antonio is another 2 hours' beyond Austin (traffic permitting). Breaking the trip up into hour or 90 minute segments can be helpful for sanity.
For scale:
DFW-San Antonio-Houston is known as the "Texas Triangle" and 75% of the 29 million people here live inside that triangle (DFW & Houston being near 50% of that total).