In Kentucky, where I am originally from, we have a dish called a 'hot Brown.' It's simple, but good: a turkey and bacon sandwich, served open face and covered with Mornay sauce and sliced tomatoes, then broiled until crisp and browning.
Although, to be honest, its usually served with ham instead of turkey, melted cheese instead of Mornay sauce, and potato chips dumped over the whole thing. It is still delicious.
Kentucky also has a native soft drink called Ale-8-One, which tastes like ginger ale. It's not bad, but I never quite understood the appeal.
As far as anything to specifically avoid, Kentucky has the same unfussy palate that the rest of the South is somewhat infamous for, and will eat just about anything that can be hunted or trapped, like frogs, or, possum, or squirrel, or literally anything else, and all the components thereof.
That said, anyone willing to prepare such a meal, and for company no less, is likely more than prepared to do so.