One of my favorite places to go in Austin. If you are a history buff this is a must.
During the holiday season Zilker Park has a trail of lights you can check out but just know it costs money to get in. The Zilker holiday tree is free though and they usually have some good food stands nearby!
SoCo is a really fun street for shopping and local food. In the evening make sure to go to the bridge and watch the infamous bats.
Another one of my favorite places in Austin, the fairly new central library! Awesome architectural design with a cool rooftop deck with great views. Also has a cute cafe inside!
If you want amazing BBQ that is right downtown this is the place to go!
If you don't mind driving a little further this is also a great BBQ out in the beautiful hill country. It is also near some wineries that you could hit up as well!
This is the "hipster" 6th street. Lots of cool bars.
6th Street is the famous strip of bars in Austin, but if you keep going East (on the other side of 35) there are even more unique bars, and a little less of a crowd.