While youre down there at the riverwalk, head to the downtown end of it, near the mall. The place where the river flows under the giant building... if you go up two levels you can get in the IMAX theater there. Then from there, you can head back out on street level, and pick up a horse buggy ride. They're not expensive, and its a bit of good fun. Usually the buggy will take you right next to the Alamo. You can get out there, and visit the historical site, or, turn down any one of the main streets there on the corner, and check out some night life. There are live jazz bands that play in the city square there too nearly every night. If youre lucky, or plan well, you can get a street side table at one of the street level eateries, grab a beer or two, and listen to the jazz, as the old street lamps come on.

Its fantastic.

And if youre in a playful mood, head north of SA and towards Fiesta Texas (6 flags)... its down Hwy 1604.

I advise not going further south of highway 90. it can get sorta dodgy down there.