Assuming you're on your own and just kinda slumming it, I would recommend some or all of the following:

Food: (I tend to stay away from chain restaurants so no Chuy's for me just a few famous local restaurants):
Maria's Tacos Village on South Lamar for breakfast or lunch. If breakfast get the breakfast tacos or migas, and for lunch get tacos, too! She has some of the most outrageous, unique salsa you are likely to find and it is heavily crave-able. It's a great dive.

Barbeque at... either Iron Works to the immediate east of the convention center, or Mueller's BBQ on Manor Road. While it's tempting to go to Lockhart for Kreuz Market, that would mean you'd be driving through the barren countryside for about an hour each way. For a one day stay, that wouldn't be worth it to me. And the 2 I've named are excellent! Get the brisket and/or sausage.

Beat the heat with Mexican popsicles at La Paletera (515 S. Congress) which has 20 fresh flavors a day. Or try Jim Jim's Water Ice for italian flavored ice. They have a main store at 615 East Sixth St and a couple carts that you may also see around town.

You might try dinner or lunch at the Alamo Cinema and Draft House (there are now 4 outlets around town including the original downtown). They have pretty good food and drink (not to mention air conditioning), plus you can watch a classic or new run movie on the big screen while you sit in comfort and chow. It's a very popular born-in Austin company that is trying to spread its concept nationally.

Recreation: I second the comment about Barton Springs Pool. Also, there's a hike and bike trail along the lake right in the middle of downtown if you're in the mood for a morning walk or jog. You can hit the pool right after a slight workout.

If you're bored and perhaps in the mood for female company of the topless dancer variety, try the Yellow Rose on North Lamar. They're also known for their inexpensive but decent steak dinners with all the fixings.

Depending on your age, you might like the 6th Street scene at night. It's mostly low 20s. There are a wide variety of bars with all different types of live music on 6th Street, between Congress and Interstate 35. In the warehouse district (west of Congress Ave. and between 6th and 4th streets, extending west for a few blocks), there's typically less live music but slightly (only slightly) older crowds with a more upscale environment.

There's a ton of live music by local acts throughout Austin on most nights. Check the listings on-line in the Austin Chronicle (auschron.com) to see if there are any bands or venues you'd appreciate. Entry fees are minimal if any. Venues I'd particularly recommend are Stubbs BBQ (usually they've got a rock band, often a well-known touring act), the Cactus (a small and historic venue on campus in the student union at UT), or the Continental Club (usually alt country). I've left out a few - there are literally hundreds of places.

Bat watching at the Congress Ave bridge will be at its peak in August in Austin. It is a sight to behold. One other idea not mentioned above is the cruise that takes you right up next to the bridge on the water. It will be a sight you never forget. It's a small investment of money (8 bucks) and time (about an hour). http://www.capitalcruises.com/html/bat.htm

Sightseeing: Believe it or not the number one tourist destination in Austin right now is the brand new headquarters for Whole Foods grocery at 6th and Lamar. It is an amazing place - google it and you can get the scoop. Austin has a proud though recent tradition as a great food destination. Before Whole Foods came along, the number one tourist spot used to be another grocery store, Central Market at 35th and Lamar. It's still a great place but Whole Foods has one-upped them, for now.