I don't know if you are flying or driving, but you will most likely need a motel.
The Dutch Village Inn is kind of pricey, but it's almost within walking distance of Timberline Dr.
Welcome to Das Dutch Village
There are also about a half dozen choices 5 miles North of Columbiana on route 7 in North Lima.
motels north lima, ohio - Google Search
My uncle just stayed at one of the off brands there, and it was a real flea bag. I can't remember the name. The Ramada doesn't exist anymore, so stick with one of the brand names if you go to North Lima.
The third choice is 10 miles North in Canfield. The Hampton Inn is at the route 11 exit in Canfield. You can catch 11 right around the corner from the Dutch House in Columbiana.
Hotel - Canfield-Youngstown, Ohio - OH - Hampton Inn & Suites
Those are your only real choices. All three towns are nice safe areas. I'm sure you can find something in your budget between the three.