Whataburger is a decent enough local chain. We eat there and like it just fine. While you are in Austin, you should give Dan's/Fran's Hamburgers a try. It's an Austin-based chain and good as well. I don't recommend PTerry's, however. I just don't get the attraction.

Outside a chain, I would really recommend Hut's on West 6th Street. Here's link to some others: http://austinburgerjoints.weebly.com/downtown.html