I say keep it simple. You want to go to some place where you can talk. Drinks are good....maybe a Happy Hour? You can always do one of the amusement parks in Vegas...MGM, Circus Circus (bring your gun), Excalibur....or maybe a local fair? (check your paper) Maybe Mini Golf.
Don't go too crazy. This is only your first date. You don't even know how much you will like each other...save the good stuff (expensive dinners, picnics, etc) for later, when it will mean more....
You want to impress her and show her a good time but you never want to set the bar too high....you'll be kicking yourself in the ass if you do. Have a good time! : )