Quick Saturday lunch between airport and Hotel Za Za?
Your route out of the airport will be Broadway to 45. Where the two intersect is a traffic circle of sorts. Exit the circle going straight on Broadway and right on your right will be Taqueria del Sol. This is actually Mexican, not Tex-Mex. Service is very quick in my experience. Continue around the circle almost full circle and exit on Park Place headed NW; just ahead on your left is a little shack called Noemi's Tacos. This will be more Tex-Mex (they do have crispy tacos, ground beef fillings) but will probably be slower. I've eaten at both and they're okay but not worth driving across town afaic.
Up where 45 intersects Loop 610 is a huge refurbished shopping center called Gulfgate and a big place called Doneraki's. I've never been but the menu definitely includes some Tex-Mex items.
Across 610 at the Main exit, which may be the one you're taking to the hotel, is Pappasito's, a part of the huge Pappas restaurant empire here. It's a chain and many hounds prefer to avoid it but it is Tex-Mex and as far as chains go, above average (I haven't been in 6 or 7 years). Portions are huge so if you want just a snack, order accordingly.
If there are specific Tex-Mex dishes you're looking for those are probably your best choices (except Del Sol) but if it's just Mexican in general, there would be others beyond the hotel you could run out to, mainly in the Montrose area a couple of miles away.
8010 Park Place Blvd, Houston, TX 77087