We also stayed at Travelers World a couple years ago and would again. Street in front goes directly downtown for easy access to Riverwalk. Or there is a bus stop right in front if you would rather not drive. One of the better restored missions is just down the street.
As noted above choose your route. Do not take E Southcross Blvd from I-37 due to steep up/down rail crossing. Military Dr just a little farther south is much better.