If I were to take a girl out on a first date and didn't want to go to a "nice restaurant" (as that can be a little much on the first date) and was going to for the classy casual feel, then I'd go to Storm. It's fairly new, (4 or 5 months) it's on the corner of Lexington and Hilliard downtown (behind and caddy corner to the Orange Peel). It's the shit, the food is awesome, oddly enough, their burgers are great as it is owned by the guy that used to own Poe's in Charleston and they have the exact same burgers as Poe's, which anyone who's been to Poe's will tell you are awesome.
It's also a Rhum bar, so they have all kinds of mixed drinks that are pretty good...mojitos and shit that girls really fawn over.
Has great outdoor seating and the inside is "intimate" without being too crowded.
I'd stay away from Salsa's, it's good, but not great for new dates because it's too crowded and you can sometime literally be right on top of the next table, which is awkward for a first date. It's also oddly bright in the restaurant.
If you're trying to impress I'd go to Red Stag or Rezazz, both are in biltmore village and both are wonderful. Other suggestions are some things other's have suggested...Zambra's for tapas (there's a new tapas bar on Biltmore ave near pack square but I haven't been yet), Sushi is never a bad idea, Mela (indian food) on lexington is good and there are a few other restauarants right next to Mela that could be good as well.