For trout in a river, the only option I remember is Guadulupe River below Canyon Lake dam. Truthfully, coming from NM and CO I was not that impressed with the trout fishing below canyon lake dam.
Don't restrict yourself to just trout. There are outstanding fishing opportunities all over TX. Chrystal clear rivers in the hill country, farm ponds/stock tanks every where, saltwater down on the coast. I tried to hit them all with my fly rod while I was stationed at Fort Hood.
Hill country - you have to get a book called Fly Fishing the Hill Country. It details access point to all of rivers in the hill country. Outstanding resource.
There are some great river and creeks in the TX hill country. Be prepared to catch 3 or 4 types of bass, many types of bream, 3 types of catfish, carp, drum, gar, white bass, crappie, etc. My favorite place was the Llano river near Llano TX. There is great fishing there with 100 fish days being common. Get there early fish until it gets too hot, then head back to town for some Coopers BBQ. Coopers is one of my favorite BBQ joints in TX, try it if you are in the area.
Farm ponds - if you can get access to a nice pond, you are in heaven. The bass and bluegills grow big and hungry in those ponds.
Saltwater - my most favorite type of fishing is fly fishing for Red fish in the flats. It is a cross between hunting and fishing. You have to spot them, sneak up on them and put the fly/bait right in front of their nose. They fight better than any trout I've ever caught except samon. Huge fun! There are all kinds of fish on the flats that are fun to catch.
If you want world class trout fishing head over to AR.
