Central Ohio is full of paddling options. There are many miles of paddling available along the Alum Creek, Big Darby Creek, Big Walnut Creek, Olentangy River, and Scioto River plus some lakes and reservoir if you would prefer still waters.
This map is for reference only, please do your own due diligence when planning a paddling trip.
Check out Ohio DNR's Paddling page for some great information and resources.
The City of Columbus also has a Olentangy Water Trail brochure with detailed information.
Real Time Water Temperatures from USGS available here