There is a room in the Athenaeum i think its really cute. It looks like a rustic chapel, maybe you could rent that as well.
You can try for one of the Dept of Rec's parks... http://www.columbusrecparks.com/rentals/Wedding%20Rentals/index.asp
If you do choose somewhere outdoors and downtown... I would make sure that the site will be cleaned if they are having Red White and Boom viewing there the night before (July 2 until midnight).
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