There are some small cabins along the north side of 67 before you get to Glen Rose coming from Cleburne with rental cabins. I pass them all the time and I think they are right by the Brazos as it crosses there, maybe adjacent to the canoe rental. Anyway . . . right along in there.
And, if you rented there, you'd head down 67 a bit farther and hit the little highway that runs by Squaw Creek Reservoir and then into Granbury. You'd have a lot of lakes and rivers to access from there: Lake Granbury, Squaw Creek, Wheeler Branch, the Paluxy River and the Brazos.
Granbury used to have quite a few bed & breakfast establishments, Glen Rose, too, as I recall. Worth a look.