One trip that I feel is worth the money if you are in Japan for any significant amount of time is a trip to Hokkaido. Hokkaido has wonderful hot springs, food, and natural wonders (yes, wonders!).
The difficulty of a trip to Hokkaido is that everything is very spread out and it may be a good idea to just rent a car and be ready to drive long distances between attractions (enjoying soft-serve ice cream made with Hokkaido milk, cheese, and other local delicacies along the way).
A destination I would like to highly recommend is the Ainu Museum. I have been there and can attest to the beauty of the area and the educational value of the trip and performances. One performance can be seen here below of an Ainu musical performance.
The museum is within walking distance of Shiraoi Station on the Hokkaido Railway as well (if you choose not to rent a car.) To put a little perspective on distances, the museum is a little over 3 hours from Hakodate by car, and over an hour from Lake Toya and Lake Shikotsu (if you happen to be visiting one of those locations). You can also get there in about an hour and a half or so if leaving from Sapporo. I imagine most first time visitors to Hokkaido will spend at least some of their time in Sapporo so this can make for a great day or half-day trip.
Admission is currently 750 yen for adults and less for kids. That’s less than US$10. Parking is only 300 yen.