Columbus!
There a few cool things to see. The Ohio State University campus is cool to see, and Ohio Stadium if you like sports. If you want to check out a movie in a cool theater, either
Gateway Film Center (which is very close to campus), or the
Drexel Theatre.
Depending on when you're in, there may be some cool festival happening at the time, and there are also so decent museums. The
art museum recently had a lush new wing built/opened, and then there is
COSI, which is a cool interactive science space, although admittedly I haven't been in some time, but remember it being fun.
The Short North area of town is very cool as well. Plenty of boutique style shops and gastropubs/higher end restaurants
In terms of places to eat:
The Crest - My fiancee and I's favorite brunch spot
Schmidt's in German Village - Authentic German food (stay for dessert for the cream puffs)
Thurman Cafe - Home of the Thurman Burger
North Market - Public Market, I've heard
Hot Chicken Takeover is phenomenal, but haven't been myself
Lola's - Gahanna Italian restuarant. My fiancee and I's favorite spot
Ringside Cafe - Best burger in town (or at least up there with Thurman)
Lindey's - Always hear about this place, but never been
Jeni's Ice Cream - best ice cream in town
I could go on and on with the places to eat...