For bars I would suggest avoiding 6th street and going straight to 5th/4th street. You avoid the college kids (mostly) and get to hit some nicer places. One in particular I would suggest is "The Speakeasy". It's pretty hard to find (the entrance is down an alley) but it's a fantastic bar.
As for places, since you're going in May I would suggest Barton Springs. It's a set of natural springs that has been converted into a pool. It's super cold, which is pretty nice in summer. And, if you're a bit adventurous you could try out the green belt, which is a massive park/forest.
I would also suggest that you go check out the University. UT is one of the biggest Universities in the world and it's crammed into 6 x 6 blocks (more or less). It's worth seeing.
trying to think of other stuff.....can't really. Maybe the capital building? South Congress? The thing about Austin is that it's less a place to visit and more a place to live. There are few single attractions that stand out on their own. It's more the fact that the entire city is amazing.