Spend the morning or afternoon swimming at the Barton Springs and enjoy how surreal it feels to swim in natural springs in the middle of a bustling city 

Walk around Bouldin Creek there are a bunch of vintage stores with a bunch cool and retro clothes, shoes and even memorabilia 

Check out the local music scene and even go to one of the local bars that have line dancing on certain nights (really make you feel your in the South )

As a cultural and artistic city, Austin has a lot of art and culture on its streets and walls but if you are looking for something more concentrated here are a few museums to visit: 

Take a hike around the famous Lady Bird Lake and get gorgeous views of the city 

Walk around the SoCo (South Congress Avenue) neighborhood they have a bunch of restaurants and shopping, it also has a lot of art murals