If you want to stay away from anything too touristy, I'd get away from Union Square as quickly as you can.

There are so many places, it's difficult to know where to start. Check them out on Yelp or Zagat. Some favorites of mine, which aren't too touristy, are Range, A16, Terzo and Skool. They'll all be easily within your budget, even allowing for cabs to and from, if you don't go crazy with the wine and shouldn't be too full of tourists.