Basically the deal with Austin is that all of the cool people in the entire desolate expanse of Texas have moved here. There is so much music that there are stages for people to play music on in laundromats.
Cops here are terrible. [User:TheWindAnd Rain] got a ticket for hitchhiking here and in San Marcos and now has warrants out for his arrest.
Although Austin can be defficult getting out of, it's not impossible. If going South and budget allows, consider a dirty dog bus ticket to San Antonio for 20 bucks. If not, you can take the local busses to the farthest point south (and outside of the city limits to avoid thewindandrain's experience).
Take bus number 3 all the way South to the Walmart in Southpark Meadows. Connect with the 210 and take it 1 stop to the high school (tell the driver you want off at the Circle K and save yourself a 1-mile walk). From there you can hitch directly on I-35 just after the bridge crossing Onion Creek, roughly 1,000 feet south of the Circle K. It is a high-traffic zone so be prepared for a 2-4 hour wait for a ride.
NOTE: underneath the bridge is a fantastic urban art gallery with spectacular work. Do yourself a favor and check it out or even consider camping there for the night. The creek is clean and beautiful. Locals are quite friendly.