Threadgill's is kind of meh for me. I like
Texas Chili Parlor for the atmosphere and the Frito Pie, but stick with the Texas Style (no beans) stuff there, imho.
Terry Black's on Barton Springs Rd is good BBQ which you don't have to stand in crazy long lines to get (just don't show up late in the evening, they do run out of some items).
Bufalina - Authentic Italian style pizza, cooked in a wood fired oven.
If you really want to research and get more opinions, just check out the r/Austin eating discussions here:
https://www.reddit.com/r/Austin/wiki/bestofaustin#wiki_restaurants
Be sure to note the Taco Map. If you are wanting Mexican food here, the best stuff is from small trailers and hole in the wall places that aren't hip or cool. Tex-Mex is of course common amongst the bigger trendy places.
Trying to pick just one in general is tough. If you could be more specific on the details and your preferences, then I can help you tailor a much better food plan.