Leon and Stellas place is lovely. Its very clean and comfortable and the bed is in the cutest little nook. They provide some bathroom and kitchen essentials for you and even put some bits in the fridge. Its in a very quiet neighborhood so is perfect for a good undisturbed nights sleep. It also has on street parking right outside.
The apartment is about a 30 minute walk from downtown Austin. Closer than this is South Congress where you can rent a city bike which I recommend as the way around as there are plenty of places to dock your bike and pick it up when you are ready to go again.
There is so much to do in Austin, its a city but with country activities available. We didn't feel like we spent enough time there.
I recommend watching the bats from Congress Bridge, its an amazing display of nature. Go rent a kayak or paddle board on the river and swim in the blue tropical looking water. Go get a voodoo doughnut. Eat at a trailer. So much to do, so little time.
Keep Austin Weird.