I highly recommend a place called "Oouchjuku", it's an ancient village with thatched roof houses:
Aizu is another beautiful area in the country. http://en.japantravel.com/view/aizu-wakamatsu-castle
Mandy, what exactly are you interested in? I would also recommend Aizu if you are interested in samurai history. The castle is very impressive and there is also the famous Byakutai legend about a group of young boys that comitted suicide when they thought the castle had fallen.
Otherwise, if nature is more your thing, definitely check out Bandai. Beautiful lakes and hiking in the mountains.
There are a few safari parks around Japan. One is in Nihonmatsu in northern Fukushima. Or get your aloha on at the Hawaiians indoor mega water park!! Say hi to the Hula Girls for me!!
Trifina, I've been to that village but I couldn't remember what it was called! Thanks for reminding me of the name. It's a really pretty place to visit and the souvenir shops are great - there's a huge selection of crafts available there.
I second Justin's suggestion of the Bandai plateau, if you want to spend time outdoors. A group of us went camping on the edge of Lake Hibara. The campsite offered a range of activities, including canoeing, fishing, mountain biking and rafting. It's a beautiful area.