Rivers are, I think, the best fishing places, but getting to a river can be difficult.
There are also different rules on different rivers regarding which parts of a river bank, if any, the public can access.
For instance, on the Brazos River it is my understanding that once you gain legal access to the river you can also access the banks below the normal high water level. So, if you get into the river without trespassing on private property you can walk along the banks, below the normal high water level. There have been confusing rulings on where that water level is though, and if you walk on the bank adjacent to private property...well that landowner and even the local law enforcement may not understand the laws...so think about whether it is worth it or not.
On the Guadalupe River it is my understanding that there is no right of way on the banks at all, the landowner owns the land down to the water regardless of what the water level is on any given day. In that case - stay in the boat or stay in the water.
Then there are creeks. Creeks are owned by the landowner. Wading or boating up a creek - or in other words, water that is not considered a "Navigable Waterway" by the state, is trespass.
You have no rights to trespass private property to get to a river, and that can make access difficult. If you can get permission from a landowner that's okay. My understanding is that where a highway crosses a river the highway right of way can be used to access the river. And there are places you can pay to access. TPW has leased two places on the Brazos River above Waco where you can access the river by purchasing a permit. There may be other areas on other rivers.
And of course not all stretches of all rivers are great for fishing. The Bosque river, for instance, is typically a mud bottom river and in many places not really very navigable with a boat. I'm not aware of any excellent wading places in it, but there may be some isolated ones. From Lake Waco up river about five or six miles a small power boat can handle it but then it gets too shallow and narrow.
From about where Aquilla Creek enters the Brazos above Waco the river is okay for boating but not all that great for wading, and the closer to Waco the less okay it gets until by the time it reaches Waco it is overall too deep.
Where Highway 16 crosses the Brazos just below Possum Kingdom is a great place to access the river. There is a parking area and the river, when low which it usually is, is great wading with clear water and a clean gravel bottom. Trout are also stocked there in the winter.
There is a section of the Guadalupe below Canyon Reservoir that is stocked with trout year round, and from what I hear - haven't been there yet - it can be excellent trout fishing as well as the usual warm water fish. There are private access points that you can pay to get in the river along that stretch and at least one public one.
The Trinity gets a lot of canoe and kayak fishermen in the DFW area and there are several places to get a small boat in - but it is a mud bottom river and it isn't likely that there are many, if any at all, good places for wading. It also catches all the storm water runoff from DFW and a lot of sewage discharge, so even if there were good wading places I'd not wade in it.
And there are other rivers to check out. Texas has 15 main rivers and 3,700 named streams. There's probably some running water near you that you can get to and fish with some research.
The Texas river laws are confusing, do your homework before you go. Here's a good place to start that research.
I'm lucky, I get to fish a beautiful stretch of the Brazos - I'd rather fish it than any lake I've ever been on - and I've been on quite a few. Give river fishing a try...maybe I'll see you out there some day.