I just spent a week in Austin with my wife and daughter. We had a great time and ate a lot of really good food, although we didn't get in much BBQ. Here's a rundown of the places we really enjoyed, in no particular order.
GourdoughsFresh, made to order doughnuts from a trailer. These were insanely good: tender middles, crisp outsides, great toppings. They are quite large though. One is plenty for one person.
Gourdoughs is in the same parking lot as
Odd Duck, a "farm to trailer" place, which looks really interesting. Unfortunately, we went to Gourdough's on a Monday, when Odd Duck was closed.
TacodeliWe really loved this taco stand. Between the 3 of us we tried 7 tacos and their queso/guacamole/salsa dip. Everything we tried was great, but our hands down favorite was the mojo fish taco.
The Mighty ConeAnother trailer. This one serves fried shrimp, chicken, avocado (or a combo) in a tortilla with slaw. Their breading is a mix of sesame seeds, almonds, chili flakes and corn flakes, which is really interesting in a good. They also have "sliders" (that are really just mini burgers as opposed to a true slider) and fries.
PecheGreat cocktails. We had just one each, so it's hard to say definitely, but based on that one, I'd put it on par with Bar Deville in terms of quality. Their food was also excellent. Their charcuterie plate included the best chicken liver mousse I've ever had. My entree was pieces of braised lamb, lightly breaded and fried, then tossed with a spicy tomato sauce over spaghetti - excellent. My wife had the coq a vin, which was also great - although the best part of that dish was the wild mushroom bread pudding that came with it.
Enoteca VespaioThe more casual sister of Vespaio mentioned upthread. We stuck to the Italian thin crust style pizza and antipasti, but they also had quite a list of house-made pastas. Great food, nice atmosphere and kid friendly. This is the kind of place we'd come back to all the time if it was in Chicago.
Blue Dahlia BistroWe were here for lunch on our last day and it was really nice to have some lighter salads and sandwiches to balance out the meat-heavy week.
FrankWe hit Frank for brunch, which I think was a mistake. Their brunch was good, if pretty standard brunch fare. But the real appeal of Frank is Hot Dougs-style sausages in a bit nicer atmosphere (very casual, but with table service vs counter service) and with beer. I didn't do enough homework and assumed the brunch would include at least a few of the sausages as options - it didn't.
In the non-food arena, I really suggest the Zilker Botanical Gardens, Nature & Science Center (in Zilker Park), Umlauf Sculpture Garden, Barton Springs pool and canoeing on Town Lake. The Austin Children's Museum was great too, if you have kids.
Edited to add: A big thanks to germuska for recommending several of these to me.