Cleared up some space.
I've spent some time talking to some of the guys at The Outdoor Source recently inquiring about that actually. From what I gather, the Scioto is pretty good along with the Olentangy (guess they released some water there today which created some whitewater conditions). I'm just now starting to really look into good places to go, but I'll try to provide more info as I get it. One thing that a lot of people do is kayak and canoe down the Scioto River all the way to Portsmouth, but that takes a few days depending on if you do the whole trip. Some go from Columbus to Chillicothe and some just do the Chillicothe to Portsmouth leg.
The weekend of the 20th, there is a 2-day trip down the Ohio River near Cincy that seems pretty fun. First day is 12 miles, and the second is 8 miles. They go through a 20' lock as well which seems like it would be pretty cool to do.
The Outdoor Source does a kayak demo every Thursday starting at 7pm at either Griggs Reservoir or Hoover. This week is at Griggs Reservoir and next is at Hoover. It's open to the public and you can try out any of the kayaks they bring out. I used 5 different ones last week, the most expensive one being $1800...I got out quick.
I'll try to get more info on some of the more current-based locations like Trapper John's.