Hachinosu Campground (map) in Kitago has tennis courts, a few other sports facilities, and a huge playground for kids. There are some awesome two-story cottages that you can rent out that are fully equipped with a kitchen and futon sets. Piping hot onsen water flows from the taps and these cabins are a great place to throw a party.
Oshima is an island of the coast of Nichinan with cabins you can rent to stay in. The cabins are situated on a cliff overlooking the ocean. They are also equipped with bedding, full kitchens and baths. There is a shared barbecue area perfect for striking up intercultural relations with other groups.