We love going to McKinney Falls for hiking. We almost always take company that visits for hiking or swimming.
Becky loves going out onto Barton Springs and Lady Bird Lake. This is the spot she usually rents kayaks. Groupon often does a deal so it might be worth double checking before you go.
Fun fact: Austin has the largest urban bat colony! You can view and hope to see the bats leave at dusk from the bridge or take a tour on a boat and BYOB. They don't feed every night, but when they do, millions of bats exit from under the bridge. It's quite the site!
Barton Springs and Zilker Park are landmarks you should definitely check-out.