Black Sheep Lodge claims to have the #1 Burger in South Austin between Kinney & Oxford and I would have to agree. While I haven't tried all the burgers in Austin, or even South Austin for that matter, I would definitely rank them in the top 5. I ordered their standard burger so that the burger wouldn't be over shadowed by all the toppings and I could really tell how their burgers were. It was juicy and delicious! You have a choice between a white or wheat bun and the wheat is fantastic. One downside is that any additional item you want on the burger(even including cheese) is an extra charge. The $6 burger can get up to $10 in no time, which turns me off a little bit.
I also ordered an item that isn't on the menu, but was recommended to me by a local Austinite. The tater tot nachos, or the Tachos, is a bowl filled with tater tots, chili, their green chili queso, sour cream and jalepenos. They're fried, cheesy, meaty goodness in a bowl. I had some other people that were there with me try them also and everyone liked them.
They have a drink special every day and an awesome beer list with a ton of local beers on draft and in the bottle. Wednesday's are White Trash Wednesday which is $1 White Trash Cans (Lone Star and PBR Tallboys, Schlitz, Pearl, Etc.). Its tough to beat a tall boy of Lonestar that's only $1!
All in all, I would recommend the Black Sheep Lodge. Its a cool hangout with good food and great drinks.