Been a number of years, but we stayed at Travelers World and would again. The street it is on goes straight into downtown and easy access parking for the Riverwalk. Or there is (or at last was) a bus stop right in front of the RV park if you prefer not to drive downtown.
But if you are arriving on I-37, do not take E Southcross Blvd. There is a rail crossing with a steep up and down over the tracks and likely cause a dragging rear end on that 5er. Take SE Military Drive from I-37 instead. No problem there.