If you're coming to Austin for just a few days, there are a few must-see stops and mostly free things to do in Austin Texas that should be part of your itinerary. Every Texan should see the State Capitol and State History Museum — and non-Texans will find it enjoyable it as well. Plus there some great historical, educational, architecturally significant, and just plain 'gotta see' downtown attractions as well. Plus, most of these are free things to do in downtown Austin. Top 10 Things To Do or About Austin