Put "Barton Creek Greenbelt Trailhead" into Google Maps for a great place to park and hike the beautiful Barton Creek Greenbelt. Head towards Sculpture Falls (1.6 miles / 30 minutes) for a really special treat, especially if the water is flowing. Head all the way to the Hill of Life Dam for a nice waterfall and swim area. Consider going up the Hill of Life if you want a rugged climb up and down. There are many other greenbelt paths, even some that will take you all the way to Zilker Park.
Austin always has live music somewhere! From the mega Moody Center to tiny bars on 6th street, you're sure to find something you'll like. ACL Live is a great venue. Stubb's BBQ has a large outdoor amphitheater with some great acts. Check out the historical Broken Spoke for some true Texas honky tonk. The Continental Club is great. Antone's is a classic.
Zilker Park used to be one of Sam's favorite places to go "frolic" outdoors. Huge grassy areas, lots of hiking trails, botanical gardens, disc golf, and the spring-fed Barton Springs Pool are some of the highlights. If you have kids, don't miss the Alliance Children's Garden, Liz Carpenter Splash Pad, and/or the Austin Nature & Science Center (the Thinkery in East Austin is also amazing for kids).
Consider stopping here if you need to kill some time between the wedding and the reception - it's three blocks from the reception venue. This beautiful building is free to enter and take a guided or self-guided tour (be prepared to go through security with metal detectors). The grounds around the building are beautiful with many outdoor memorials worth visiting. Waterloo Park, a block east of the Capitol, is another great place for a stroll.
Texas is known for it's brisket! We agree with most of the recommendations in the below link, but don't rule out Rudy's on 360, just down the road from the church - great casual spot for a gas fill up and some amazing BBQ.
So many good breweries in Austin, we could do an entire page on them! Pinthouse Pizza has great pizza and their own beers as well as many more on tap, The Brewtorium in north Austin has incredible salads and pretzels and beer, Nomadic Outpost is a cute little place south Austin, The Stay Put is a small nice place on Rainey street, Live Oak is fabulous and near the airport, Central Machine Works is a large brewpub in a repurposed machining building, Hold Out Brewing has really good beer and food, Jester King is a bit of a drive but well worth it for a sprawling venue with outdoor games, pizza, goats, kids playground.