I'm from Ohio, even though I live in Michigan now. The two states are very similar, even though Michigan is technically blue and Ohio is technically red. The reality in both states is that more rural communities tend to be more Christian and therefore more queerphobic. Ohio edges out Michigan into the red zone by having more significant rural and small-town populations.
In deciding where to live, consider that largish and mid-sized cities are more likely to be queer friendly. Toledo comes to mind as a small city that isn't well known but is pretty darn nice. It's also quite a reasonably short drive from Ann Arbor, Michigan, which is very progressive and lovely. So if you're looking for affordable places to live, lots of little towns between Ann Arbor and Toledo offer low rent and queer comfort — or at least reasonably easy access to queer comfort.
You might also consider the Dayton area, or more specifically small communities between Dayton and Cincinnati. Cincinnati is quite progressive, but rents are not necessarily low there. Heading north toward Dayton can get you into the best of both worlds.
Also, think about suburbs/exurbs of Cleveland or Columbus.
Avoid Akron, Canton and other small rustbelt cities to the west of the state. That area can offer very low cost of living, but populations tend to be intensely and intractably conservative.
Sorry, I know that's not really on point to what you were writing about, but I wanted to throw in my personal two cents from lots of Ohio experience.