We love to frequent Barton Springs when it's warm and sunny out. Barton Springs is a natural pool directly next to Zilker Park with a view of the downtown skyline.
There is a strip of restaurants and shops along South Congress Avenue that is fun to walk and explore. You can find anything from Hermés to local Austin art here. Look north up the road directly to the state capitol building.
Lady Bird Lake, which runs through downtown Austin, is a great stop if you're interested in a walking/running trail or renting a kayak or stand up paddle board.
6th street is an Austin staple if you are looking for some nightlife while you're in town. All areas of 6th street are walkable but you will want to take a rideshare to get there and back home.
Some of our favorites are Terry Black's BBQ, Odd Duck, Loro, El Alma, Paper Boy, Ramen Tatsu-Ya, Chuy's, Torchy's Tacos, and tons more.