Being a resident of NE Ohio I'm bias. And I've only been to Myrtle Beach once...when I was 10 and I didn't like it. So forgive me when I start boosting the tourism for NE Ohio!
We camp every year at Cedar Point (first week in September our local
AAA club offers special discount tickets). Campground is basic, unless you pay for the "premium" sites that include cable. (These are the pull through sites, and are really nice...you even have a type of lawn, not just grass!) Bathrooms are fine, and even nicer when you stay in the premium area, and it's nice to be able to get into the park an hour early to ride the Millenium and the Top Thrill Dragster.
The other campground we've stayed at was Bayshore. It's right off the entrance of the park, has tons of activities for youngin's to do do, a great pool, and boat launch access.
Not much else to to in the direct area though. You do have Put-in-Bay and Kelley's Island for some nice wine and history. Cleveland's not that far off.
If your'e doing two weeks, I might suggest a stop at Geauga Lake (in Aurora)on your way to Cedar Point. They also have their own campground (pay for the pull through site, trust me on that one!) and the admission is extremely cheap for a thrill park and water park in one. Stay here for a few days and you can easily drive to Cleveland, visit the Zoo, the Science Center and the Rock and Roll Hall of Fame; everything is within a 45 minute drive. Then head on to Cedar Point.
But that's just me!