The River Walk is always a fun place. If you go up to street level there are horse and buggy rides and usually the driver will give you a tour of landmarks in the area, which is pretty interesting! Menger Hotel is neat, it's right near the Alamo. I wouldn't waste my time with the mall, it isn't so great, there are some cute shops at street level, though. You can also take a river boat tour of the River Walk, or a dinner cruise, I have gone on the tour during Christmas time and it was gorgeous! They aren't on the River Walk, but my families favorite restaurants are Papasitos and Papadeaux, with google maps they are relatively easy to get to!