Define big chain.
Personally, for my weeknight BBQ needs, I like Rudy's (usually the one closest to you on 183). Their extra moist brisket is... well... extra moist. Tasty, smokey, usually has a good smoke ring on it.
Their potato salad is... akin to what you buy pre-made in a grocery store, but I dig their beans and their creamed corn moves me.
Welcome to Austin!
In the Arboretum area, I like the following:
Eddie V's, Steak and Seafood
Musashino, Sushi in the evening
Mikado, Sushi and Bento Boxes for lunch
Asian Fusion type affordable lunch, Firebowl
Can't recommend any BBQ except Rudy's (chain) if desperate. Order the moist brisket.
Jersey Mikes, Sandwich.
Breakfast, La Madeleine ( another chain. A couple of miles north on Jollyville Rd is Kirby Lane. It's rather "Austin", but the service stinks and I think the food is okay at best).
Many of these have very good happy hour options, as well.
I hope you enjoy!