Look up places that have been featured on Diners, Drive-ins and Dives. Flavortownusa.com lists all of them. They are usually really frugal, a good example of local eats, and great-tasting.
We have a "road trip rule" that we don't eat at chain restaurants, or at least ones we've been to before. It's all about exploring new places, so no McDonald's or Olive Garden for us. Sometimes when you want a quick bite to eat that can be challenging, but it's worth the effort to try new things while on the road.
The kids aren't allowed to order the same thing two days in a row. Too many children's menus offer the exact same thing: hamburger, chicken strips, etc. This way, they don't get stuck in a rut.
We use the YELP app to search out local places as well.
We like to recognize the most adventurous eater or strangest thing eaten. It's fun to point out on the menu things we've never eaten, or sound exotic or strange in some way.
Stop at local grocery stores to check out regional differences. Try new things, whether it's a different brand of potato chips or local flavors from the deli counter.