Austin's restaurant scene has really exploded in recent years and it's hard (for me, at least) to keep up but here are a few that have been around for a while that we typically take out of town friends to:
nice traditional (kind of french american / steakhouse) -- jeffrey's
sushi / japanese / james beard winner -- uchi (my longtime favorite in Austin -- uchico is great too but i prefer the smaller original uchi)
fancy-ish bbq / Texas food (maybe not top tier bbq (save that for franklins, valentina's, etc.) but everything els on the menu is very good) and good downtown / walkable area -- lamberts
good italian south congress walkable -- vespaio
good seafood south congress walkable area -- perla's
good seafood not quite as walkable but pretty close to other bars / restaurants -- clark's
nice southern (and i think a james beard finalist) -- olamaie
Jeffrey's, lamberts, perlas, and clarks are part of the mcguire moorman group (they also do elizabeth street (good vietnamese) and a few other places you can check out on their website). They're pricey (and some would say overpriced) but i think they're all excellent.