About 1 1/2 blocks east of the Alamo there is the River Center parking garage with several stories. pay parking
or, across the street from it, there is a large open parking lot (pay parking)
From Ft. Sam, you can go West to N. Alamo Street, then stay on it all the way downtown. You'll pass the Alamo on your left. Turn left on Crockett and go east until you see the parking lots. Not far. You might get lucky and find a parking place right on the street..if you're lucky. Parking is as safe there as anywhere else. Plenty of good eating places in the River Center, just go inside the Mall.
Sorry, I get my rights and lefts turned around sometimes, lol