Rock Climbing Gym. Learn to climb a little first (tie in, belay, and such) and then take her.
Local music- coffee shop, bar, w/e. Find some local act at a small venue. Usually it's cheap/free.
Go snowshoeing or cross country skiing. Try downhill skiing or snowboarding.
Sledding at a local hill. Sounds dumb, but isn't. (Try it in the summer using a cube of ice instead of a sled, but be prepared for grass stains and mud.)
Movies
Ice Fishing.
Art Gallery, if she's artsy...Check your local university. They should have tons of them. They also will have band and choir concerts. Percussion ensembles and jazz concerts are usually pretty decent even for non-music lovers.
Go to a play. Pick a comedy show, a night of one-acts is usually a good choice.
Local Sporting Event. HS, College, Pro. W/E.
Swimming at an indoor pool. Preferably one with a sauna and hot tub as well. Outdoor Saunas and hot tubs can be fun in the winter too.
That's all I've got for now.