Tallahassee FL is a very underrated city. Most people think it is just the capital of Florida but it has much more to offer. There are thousands of hiking areas with various terrains. This includes forests, swamp lands, and lake hikes. There are also a wide variety of mom and pop restaurants throughout the city.
St. Augustine FL is the ultimate family destination. You can find things that little kids will be interested in (like the ghost tours), things for teens (the fort), and things for adults (numerous bars and restaurants). The best part about this is everything is relatively cheep as compared to Florida's other attractions like the amusement parks.
Charlotte NC has a wide range of activities for you to explore. You can wonder through Romare Bearden Park and explore the wooded area across the stream or take a stroll around the pond. Just a ten minute drive from there, there is a downtown area where you can catch a minor league baseball game, lie out on the grass area in the park right downtown, or visit the restaurants surrounding it.
Durham NC has many local restaurants. If you are looking for a doughnut place I would highly recommend Monuts. They have the best doughnuts I have ever tasted. Also located in Durham is the Duke Garden. You could spend hours getting lost in this garden and never get bored.