What little public hunting there is in Texas, is generally by application and draw in very limited areas. In the Hill Country (Austin and west area) there are usually at least a thousand applicants for very few permits. The Parks & Wildlife has a pretty good synopsis of the areas on their website. When they say hunting is by "compartment", they mean you get an assigned area to hunt and that's the only place you can hunt, no matter how big the wildlife preserve is. Not all are like that, but most are. I have bowhunted a few places and it can be anywhere from good to miserable. Just depends on the area.
Farther to the south, San Antonio and south, there are a lot of ranches that offer deer, hog, and exotic hunting. Of course you have to pay. Nice thing about exotics is that you can hunt most of them year round. Some places have reduced rates for groups so it might be an opportunity for several of us to put together a package deal.
Gary, my son lives in Austin. He can probably offer some general advice for getting around the city, if you need it. Let me know.
Are you (or anyone else) going to the RMEF show in Ft. Worth in March?