You and I may overlap briefly in SA.
See The Alamo, obviously, if you haven’t before. River walk is best in the morning before things open and it gets too hot. If you like to jog, it’s great for that. Maybe go for a jog and then fill up on an old school cheap Mexican breakfast at Taco Haven to give you fuel for the day. It’s a bit off the Riverwalk on the convention center side.
Best Mexican food won’t be on the river walk. Mediocre Tex Mex there, but still probably better than what you’ll find in most parts of the US.
If your downtime is truly significant, make a day trip up to the hill country. SA, like most Texas cities, is enormously spread out. After a couple trips, downtown can get pretty tapped out. I hit the zoo last time, but only because I had my kid with me.