Kakuda Space Center is located in Miyagi Prefecture. It is an actual JAXA (Japan Aerospace Exploration Agency) facility which researches how to take humans and technology into the depths of space. Also on weekdays it displays public exhibitions of rockets and engine parts. The best time to go is during their biannual open houses during Science Week in April and around Space Day on September 12. During this time additional research facilities are opened, tours are given, and you can participate in activities such as sampling space food or building a water rocket. Enjoy the pictures from a previous open house.
More information can be found on their English website: http://www.jaxa.jp/visit/kakuda/index_e.html