Stubb's not only has great grub but they've also got a great line-up of musicians. Any given weekend, you'll see lines out the door waiting to go in. For music line-ups, check out the local Austin Chronicle or their website.
Their food is also excellent. Their brisket is very tender but I go there for their chopped beef sandwich. It's saucy and not as greasy as most other places. A plus, if you go into their outdoor music state, they have a stand where you can buy a sandwich, chips, sodas and beer while you wait. Perfect for after-work music.