As Nicole advised, the WeddingWire venue directory is a great place to search for that perfect venue. You mentioned you already searched the directory and couldn't find anything. Were you searching in Columbus? I've found a nice collection of venues there for you - Columbus Wedding Venues
These venues may not explicitly say on their storefronts they're pet-friendly, I'd imagine you would need to reach out to them directly to ask this. You can narrow down this down further by venue type, capacity, setting, amenities, etc, and contact them via WeddingWire
What pets are you involving in your big day? How will they be a part of the celebration?