Indiana can play their H.S. championships at an NFL venue as can Xichigan and Ky. play their H.S. championship at an SEC school but Ohio has none of those options other than Canton something just doesn't seem right.
Other states make it a priority to get the best venue.
Maine - NCAA D1 FCS (1 game of 4)
Massachusetts - NFL
New Hampshire - NCAA D1 FCS
New York - NCAA D1
New Jersey - NFL & NCAA D1
Maryland - NCAA D1
Delaware - NCAA D1 FCS
Virginia - NCAA D1 FCS (two venues, out of three)
North Carolina - 2 different NCAA D1s
South Carolina - some at NCAA D1
Georgia - NFL
Florida - NCAA D1 (though moves around some)
Alabama - NCAA D1 (rotates around between Bama, Auburn and UAB)
Mississippi - NCAA D1 (rotates between MSU and Ole Miss)
Louisiana - NFL
Arkansas - War Memorial Stadium in Little Rock (some NCAA D1 games are/were played there)
Missouri - NCAA D1
Indiana - NFL
Michigan - NFL
Illinois - NCAA D1 FCS (currently played at NIU and SIU)
Kentucky - NCAA D1
Tennessee - NCAA D1 FCS
Wisconsin - NCAA D1
Minnesota - NFL
Iowa - NCAA D1 FCS
North Dakota - NCAA D1 FCS
South Dakota - NCAA D1 FCS
Nebraska - NCAA D1
Kansas - (don't ask)
Oklahoma - NCAA D2
Texas - NFL
Colorado - Some NCAA D1 (others at CSU-Pueblo)
Wyoming - NCAA D1
Utah - NCAA D1
Idaho - Varies, some NCAA D1 some NCAA D1 FCS
Nevada - NFL and NCAA D1 (depends on matchup)
Arizona - NFL (for some)
Hawaii - NCAA D1 (when the stadium is available)
Montana and New Mexico play at the highest seed. Kansas plays at several small colleges throughout the state (1 game each).
Ohio, West Virginia, and Pennsylvania are odd-balls. Rhode Island plays at Cranston HS. Vermont plays at Rutland HS. Most Maine games are at Portland, not U of Maine. Connecticut plays at the higher seed or local stadium. DC currently plays at a HS stadium, though have played at RFK in the past.