I live in KY. Having said that, there are not very many campgrounds in the area immediately around Williamstown, KY. However, within 60 to 90 minutes drive, you can find sites at Kentucky Horse Park, just north of Lexington, KY and north and west there is Big Bone Lick SP and General Butler SP. The later two parks are near the Ohio River, though not within eyesight of the campgrounds.
There are places to visit on both sides of the river in and around Cincinnati, including the World Peace Bell in Newport, the Newport Aquarium and Newport on the Levy shops and restaurants. And do treat yourself to an afternoon on the newly renovated Smale Riverside park on the Cincinnati side. It extends about 7 miles and has bike rentals and lots of fun activities for adults and children of all ages, including water features. There is no charge except for parking. If your feeling like an adventure, take a supervised Segway tour from CIncinnati Bike Center... can often find Groupon discounts, but MUST be reserved in advance.
https://www.groupon.com/deals/cincin...est_ms=1023626
Smale Riverfront Park - (513) 352-6180 - Cincinnati Parks
Lexington is also a great place to visit. Lex is very close to several of central Kentucky's distillery tours, starting with Towne Branch in downtown, then Buffalo Trace near Frankfort, and Woodford Reserve near Versailles, both close to Lexington. The later two tours are on very beautiful grounds.
If during horse racing season, get a $5 admission to Keeneland Race course, second only to Churchill Downs in Louisville, but much more scenic.
There is also the private Elkhorn Campground, near Frankfort... have not been there for 25 years, but as I recall it is real close to the river.