The consensus "best 'burger in Austin" seems to be Casino El Camino. I also like Phil's, Roaring Fork (check their happy hour pricing), and Waterloo. Hut's is OK. Lots of steakhouses have good 'burgers.
We don't have any good burgers in Austin, sorry. I know, it sucks. I suggest you move back to where you came from and if you have any friends thinking of moving here, let them know of the shortage of good burgers so they don't move here either.
Juuuuuust kidding.
Depends on what you like but Casino El Camino is amazing. But know the rules. They can be like Burger Nazi if you catch them on a bad day.