The Northern Kentucky area has many great restaurants -- both independent and "chain". Two chain restaurants which are local to Cincinnati are LaRosa's Pizzeria and Skyline Chili, with locations in Kentucky, Ohio and Indiana. (Petersburg is in a tri-state area.)
Pompilio's is an Italian restaurant in Newport, KY, which is featured in a scene from the movie "Rainman". It's located not too far from Newport on the Levy, a retail and entertainment center on the Ohio River, right next to the Purple People Bridge.
The Greyhound Tavern is "Northern Kentucky's most award-winning restaurant" according to its website, and its sister restaurant Tousey House is located in Burlington, KY. Both are owned by a family who also owns homes in Petersburg and has invested in our community.
See my blog on "Area attractions" for more ideas...