I recommend Travelers World. It is just a little south of downtown right on city bus line with a bus stop right outside the front gate. Would save having to manipulate the TC downtown finding a place to park. And the Mexican food restaurant right across the street is supposed to be very good, although I have not tried it so can't really say. But I would suggest Casa Rio Restaurant on the Riverwalk if the weather is good, or Mi Tierra Cafe y Panaderia on west edge of downtown whether the weather is good or not, if you want Mexican food with atmosphere.
There is ample parking downtown near the Riverwalk where you probably would not have a problem finding a place to park if the TC is not too large. I parked my F350 crew cab long bed in two different lots there, but not with a TC on it.
Travelers World is also on the Mission Trail and very near one of the larger and better restored missions if that is of interest.