Haven't "touristed" lately , but have carried many times on the Riverwalk itself. There are some 51% establishments there, I think, but lots of restaurants and shops that are not verboten. I did see a 30.06 sign down there once, but can't remember where, been some years back, and lots of other places to go. Haven't been to the Tower of Americas since they refurb'd it, so don't know there (for all I know, the city owns the building?).
Stay concealed, have fun, behave yourself
, you should be fine.