Stiles Switch has great BBQ and they seem to have it all day and into the night. Plus there's beer and sometimes bands on the patio. If you want hassle-free, easy to get to BBQ that's great, this may be your best bet. Not sure how far it is from the airport, but it is in Austin proper. Great atmosphere.
I've heard great things about Mickelthwait Craft Meats, but have not been myself - would like to go, though.
If you get mobile - by all means I'd go to Snow's on Saturday morning (don't wanna get there later than 8am) then you can take the 30 minute drive to Louie Mueller's in Taylor. Then you need a nap.
If you can get to Lockhart for the big 3 - Smitty's, Black's, and Kruez, you'd be glad you did. This is probably around a half hour or so from where you'll be.
I really like John Mueller's Black Box BBQ in Georgetown, which is probably 30 or so minutes from the airport. Really great stuff and I think this John Mueller is kinda underrated (he seems to be a much better cook than a he is a businessman).
La Barbecue is supposed to be great, but last time I was in Austin there was a huge line when I drove by.
I think City Market in Luling is supposed to be within a half hour or so as well, but I've never been. Supposed to be great and I hope to hit it next time.
Non BBQ - Tacor More, Torchy's Tacos, Hyde Park Grill - many other good spots to consider as well.
