lmjacobs
Staying at the Hyatt Arboretum, but will have a car.
The immediate area around the Hyatt has a good bit of stuff. Congress Avenue is a hub of activity in Austin. Within a couple of blocks, you will find
Amy's Ice Creams (small chain, mostly in Austin, but also some other cities in Texas). Creative flavors, use of mix-ins, small-batch preparation. In some ways, I think that this is what Cold Stone would be if they had really good ice cream. The servers are usually a little quirky and fun - and they'll usually let you sample darn near everything in the place. Amy's is a must-stop whenever I am in Austin.
A little further up the road is a lot filled with one of the things that Austin is so noted for - an array of food trucks.
Hey Cupcake! is one of the vendors there (look for the AirStream). I am a fan of their red velvet, but I don't recall having anything there that I didn't like. There are other carts will all kinds of goodies - pies, Mexican, BBQ, etc. You could eat for hours. You may want to check, but I think that there are no Monday hours.
As for your original question, I don't think you could wrong with either choice (Threadgill's is iconic, Hoover's is becoming iconic!), but I probably like Hoover's a little better.