Anywhere from two days to two weeks.
Charleston, West Virginia is the best answer if you are looking for a big city. It is 1 hour and 40 miles closer to Cleveland, OH than to Durham, NC.
40 miles
Mount Hope, WV
Charleston, West Virginia
13 miles
From Mason OH to Cleveland OH (228 mi.) is about 4 hours driving time.
It is 515 miles according to Google Maps.
The shortest distance is 570 miles.
Charleston, West Virginia
It is 573 miles according to Google Maps.
The driving distance is about 515 road miles.