Poking around the Amish Country of Ohio, you might come across the Amish Country Scenic Byway and some of its off-shoots. Leaving from Loudonville, for instance, you'll head towards Millersburg on OH-39/60. From Millersburg, you can go to Wilmot on US-62, or down to Danville in the other direction on US-62. Also on the route would be the scenic drive from Berlin to Dover on OH-39.
A few words of caution about the Amish culture. Amish folks do not wish to have their photographs taken. So if you are wishing for some scenic photos, make sure that any Amish faces are turned away or that the people are not going to be in your photo. Also, when you are driving, slow down! They usually drive a horse and buggy, or an open cart, and horses can be easily spooked by a motor. Whatever you do, do NOT honk.
Be sure to stop in some of the towns along the way – Millersburg, Berlin and Sugarcreek are well-known places for good old-fashioned Amish cooking, and often the shoppes are run by Amish. Baked goods, candy, and quilts are among some of the purchases that friends of ours have made. Also keep your eye out, in summer and fall, for the old-fashioned produce stand.
Here is a general website about the area.
Mohican State Park, Loudonville
Other than Mohican SP, most of the campgrounds in this area are privately owned. However, for a camping experience that might be similar to the Amish lifestyle, one could camp at
Turkey Hollow Campground.
Note: This campground only accepts tents. There is one running water spigot on the property, but there are no other hookups. It should be noted that the rates are in line with public camping, but only cash or PayPal is accepted.
A few miles down the road in Warsaw, there's a little known campground next to a little waterfall. Check out:
Magical Waterfall Campground, Warsaw
Note: There is no other website for this campground.
There are any number of private RV parks in the area.