**** dog tons of places are within an hour-2 hours from Austin. But if you are coming down to see someone, dont sweat wheeling.
Austin itself is full of stuff to do without going wheeling. Enjoy the town. Party on 6th street or if you dont want to look like a local 8th street. Venture across the lake and party on S. Congress at The Continental Club. Eat at Chuys, eat breakfast at Juan in a Millions on Caeser Chavez. Take a drive on the west side around the lake. Eat at Rudys BBQ (gas station) on Capital of Texas Ave (just west of MoPac).
Check out the Austin Chronicle (free weekly press) and see what bands are where. Austin is a hotbed of music. Everything from western, rock-a-billy, Texas/RedDirt, rock, alt rock. etc...
Hit the Austin Speed Shop on S. Lamar and see what Bob Bleed or Fat Lucky are building (Jesse James owns it now).
Check out the Hula Hut and grab a burger.
Austin is by far my favorite city in North America, I would live there if I could find a job doing what I do. At one point I was in Austin at least a weekend a month for something, football, hot rods, concert, just to party, the lake, bachelor party, etc...
If you must wheel, drive west/northwest to Katemcy, its just under 2 hours.