The Tavern's burgers are very good, they make them the same way as Hill's (same owners).
Fuddrucker's - I like the choice of toppings (especially the pico de gallo) and they have an excellent spicy mustard. Very good fries too, nice sized wedges add some jalapeno cheese sauce and spud spice!
Dirty Martins - they have pretty good chilli too
Culver's - much better than the typical chain retsaraunt burger
Have not tried Casino el Camino but I would really like too, I think they were on one of those food network shows for their burgers.
J and J's Breakfast and more on Parmer lane, just West of Amherst, the intersection by Cool River. Fantastic Cheese Burgers where the cheese melts down onto the grill and browns, and that whole cheese pancake with burger in the middle goes onto the bun.
They also have a huge and delicious Migas breakfast plate and serve it all day long. Bring a friend, or take half home for tomorrow.
I lived in Austin back in 76-78 their was a Sandy's I believe on Riverside or Barton Springs across from the Armadillo (good times) I don't know if it is still there? Also frequented Hills for breakfast good biscuits and ham steaks.