I would like to know a safe stop for overnight after driving 8-10 hours

Mary has a great suggestion to stop in Charlotte, that's what I would recommend. Columbia is also a good option. If you really want to see every small town between 8-10 hours along the route, check this page:
https://citiesbetween.com/new-middletown-oh-and-davenport-fl

I assume you are largely travelling to Davenport (Florida) via the I-79S, the I-77and the I-95S?
Charlotte is about 8 hours drive from New Middletown (Ohio). The Marriott SouthPark isn't too far from the I-77: 
https://www.marriott.com/en-us/hotels/cltph-charlotte-marriott-southpark/overview/
Alternatively, Columbia is about 9 hours drive. The Marriott Columbia is on the I-77 side of the city: https://www.marriott.com/en-us/hotels/caemh-marriott-columbia/overview/
For future reference, Marriott (like all chain hotels) has a page which lists all its hotels worldwide:
https://marriott-hotels.marriott.com/locations/