Yeah Houston traffic is really rough so either coordinate to hit places close to one another or pick one place. St. Arnold's is Houston's largest and oldest craft brewery. It probably won't blow you away but you won't find bad beer, either. Karbach is also a solid brewery but an AB Inbev acquisition.
Lots of breweries in Houston make one or two good beers and the rest are not great so unless you are really committed to going to a brewery then you might have a better experience tasting Houston's breadth of craft beer at one of the better known bars. Hay Merchant, Flying Saucer, Gingerman are all good options. If you're on the north side Petrol Station is good.
Austin traffic is bad and will be especially bad around the rivers between Austin and San Antonio because of the holiday. Stay off I-35 in Austin if you can. Austin will be crowded in general with the holiday so plan accordingly.
Live Oak is definitely worth the stop. Either of the Pinthouse Pizza locations are also worthwhile stops. I like Austin Beerworks on the north side as well. I am not too familiar with some of the newer breweries like Zilker and Lazarus although I hear good things about both.
If you want the most access to breweries in Austin then the northwest side of town around the 1/MoPAC and 183 intersection will put the most around you. In that general area is Austin Beerworks, Pinthouse Pizza (Burnet), Adelbert's, Celis, Circle, 4th Tap, Oskar Blues, NXNW, and I think one or two others have opened up there. Not all of those are worth your time but plenty of options. The Whole Foods grocery store near there has a solid tap list as well.
If you want to hit beer bars then Bangers and Craft Pride on Rainey St. are the best options.
You'll find some of the Jester King shelf beers around town. Maybe some of the limited but not brewery-only releases if something came out recently. Your best options for more limited offerings are sunrise bottle shop (it's in a gas station, really) or whip-in. Specs sometimes has some good stuff on the shelves and they have locations all around town.