The Washington Post has an interesting interactive map of the most- and least-sunny counties in the United States:
Map: Where America’s sunniest and least-sunny places are
As for Ohio, much of Northeast Ohio, from Cuyahoga County all the way down to Monroe and Belmont Counties in the south, is among the least-sunny parts of the entire nation. I would imagine this is a combination of our northern location, along with cloud cover created by the Great Lakes.
In general Ohio gets a little more sunshine gradually as you go southwest towards Cincinnati - except for one area of interest: Erie, Huron, and Lorain Counties, which are the sunniest counties in Ohio, and in fact just slightly above the national average.