I’m from Texas originally, been living in Missouri since early July. Texas is kind of a crazy place for shooting and hunting. Big time hunting state and a big gun state, but you pretty much gotta pay to play and it’s not cheap. Mostly rural, also mostly privately held. Where most Texans actually live, all big city and suburbs. For good hunting or a nice range you gotta pay a premium price or buy your own land, good cheap land is available but it’s a good days drive from your home in Houston. Out where there are no jobs or economy, you will never enjoy it until you retire or unless you are a trucker. Most people can’t even afford the taxes on a nice place near the big city.
BLM land is not really a thing in Texas. Hunting is strictly off limits in Texas state parks with some exceptions, mostly drawn hunts. You do have the national forests in East Texas and they are amazing, and not too far from you to spend a weekend out there.
The days when you could just go to the edge of town and hunt or shoot are pretty much gone. They never really were unless the land around your home was already bought up with plans for strip malls or subdivisions. I grew up on the edge of a giant sunflower field in Mesquite, about 20-30 minutes from downtown Dallas, where we could do whatever we wanted. It turned into a subdivision in about two years and we never saw it coming.
Some of the Texas WMA’s allow target shooting some even have a free range. There are probably a hand full of “dove fields” leased by the state for public use very near to you. They are mostly shotgun only and no target shooting.
When I found myself living where I could not shoot in Texas, I figured out where the nearest rivers were located and got in touch with the game wardens of those counties by email. I asked very specific questions about hunting non game non protected species with airguns such as armadillos and bullfrogs, jack rabbits etc in the river bottoms of river x/y/z. Shooting targets down there, etc. I got the go ahead, printed copies of that email, and kept them in my wallet at all times so I could hunt and fish down in the Lampasas river. Parked my car in the right of way at the highway bridge and had my little adventures down in those river bottoms that were virtually untouched if you are willing to walk a mile and that means get in the water in many places. Fish that probably never bit a hook. It was awesome.
Now they have classified nearly every non game species as a fur bearer so you gotta use at least a .30 cal if you want to use the airgun. So your mileage may vary.