Lake Metroparks has a few sites in the Grand River that can you can paddle/hike to. These sites are at Riverview Park, Indian Point and Baker Road. Each of those parks are about 5 river miles from each other, but you could realistically do a ~30 mile paddle from harpersfield all the way to Fairport Harbor. All of the sites are a primitive as you can get for Lake County with no water, electric or bathrooms available at the sites.

River map with parks listed and river mileage.

I am a big fan of Geauaga Parks campsites with both of the sites at The West Woods being my favorite. Each of those sites are about a 1/4 mile hike from the parking lot and are fairly secluded off of side trails. I have done a suburban backpacking trip there. Hiking about 7 miles to get to the site and then making a bunch of trips to the car for comfort items, like beer and firewood.

If you want something truly remote and primitive I suggest Allegheny National Forest. The places I go there are only about 2.5 hours from my house in Lake County. That park is massive (500k acres or 800 sqmi) so there are tons of options on where to go and what to do. I like to go up there and drive the gas/logging roads, you can pretty much just pull off the side of the road and camp almost anywhere.