Grass fed, grass finished beef
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.
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: