Grass fed, grass finished beef
There's 2 vendors at the Wednesday afternoon farmers' market at the Triangle. One had beef and pork and I think the other had beef, bison, and poultry. Pretty pricey but the guy from the Elm Mott (near Waco) Homestead farm/school was there also with his cheeses. They teach weekend classes in cheese making, beekeeping, poultry, etc I'd like to try sometime.
I think it's cheaper to buy a quarter beef from a producer. Here's a neat link for Texas' growers, many of whom deliver to Austin:
Whole Foods does have some very nice grass fed beef (although it's probably worth asking if it's grass or grain finished). It probably varies how locally-sourced it is.
Wheatsville Co-op has Nieman Ranch beef, which is a large-scale, multi-location operation beef, but claims to be grass-fed. I've had it and it's good beef.
I haven't been to the Farmers Market in a month or so, but that's probably your best bet, assuming that beef is available again. You can talk directly to the farmers and discuss exactly what you're getting. Back a month or so ago, at the peak of the drought, none of the farms had any available.