I'm going to be traveling to Columbus for a work conference. I've never been to Ohio, so am looking for things to do and if there is any food that is particularly Ohioian that I should seek out.\
Also, what is the weather typically like in the beginning/middle of October?
I've been to Dayton twice around this time of year for airshows. Weather is typically high 60s-mid 70s though it can be chilly in the mornings and evenings. Cincinnati has terrible smog problems, so depending on weather patterns the air quality can be diminished for miles around.
If you like airplanes, the Wright-Patterson AFB in Dayton has one of the finest aviation museums in the US, and its a little less than 2 hours from Columbus on the interstate.
Don't know about the food. Seemed pretty typical to me.
My grandmother lived in Cincinnati, which is way south of Columbus, and I've been to Dayton a couple times to see the museum there. Columbus looks to be about the same general latitude as Indianapolis though, so I would think they get the same general type of weather. This time of year, its usually in the mid-70s like Neo said, though recently its been in the mid to high 80s.
As for food, this may just be a Cincinnati thing, but every time we went, at least one of the places we ate was a Frisch's Big Boy restaurant. Big Boy restaurants used to be everywhere, but I think they are pretty much just in Ohio now. They are kind of hard to describe, kind of like a super high-quality Steak and Shake? But they have like salad bars and stuff too.
I was in Columbus once for some reason in college. I don't remember what we did, but it seemed like a decent city. It's not nearly as depressed as northern Ohio.
Columbus is really nice in the fall. Don't think that because people from Ohio like Skyline Chili that it's good. It's awful. If you're there over the weekend for any reason, their football games are good. If it's this coming weekend (Oct 1) by chance that you might be there and can sneak out to watch them beat the daylights out of Rutgers, going to a game in that stadium is always worth it.