So, is it okay for someone who hasn't been to Japan to offer any suggestions?
Perhaps one option could be to visit the island of Kyushu.
The city of Fukuoka sits along Hakata Bay, where the key battles of the Mongol invasions of Japan in 1274 and 1281 took place. I believe that there is a small museum in the city which covers these events. Further inland, the Kyushu National Museum at Dazaifu reportedly takes a broader look at Japan's pre-modern interactions with China and Korea. Plus, there are ferries which head across to Busan in South Korea, if you wanted to take a side trip there.
Nagasaki may be most (in)famous for what happened there on the 9th of August 1945, but its heritage as a link to the outside world is reflected in sites like Dejima (which once hosted representatives of the Dutch East India Company) and in Japan's oldest Chinatown (which happens to hold a Lantern Festival for Chinese New Year). Plus, there is a Dutch-styled theme park, Huis ten Bosch, in Sasebo.
Further south, Kagoshima prefecture includes the city of Kagoshima itself (the former seat of the Shimazu samurai clan), Sakurajima (an active volcano which simmers across the bay from the city proper), and Tanegashima (where the first Europeans - and European firearms - landed in Japan in 1543, and where JAXA's main spaceport is located).
There is a shinkansen route running from north to south, as well as a number of "heritage" trains across the island.
Beyond Kyushu, the island of Okinawa hosts Shuri Castle, the former royal residence of the Ryukyu Kingdom, as well as other sites dating to that era. (The Shureimon, one of the gates leading up to the castle, is on the front of the 2000 yen note - which is reportedly rare in "mainland" Japan, but more common in Okinawa Prefecture). I'm not sure if there are any ceremonies of note in Okinawa to mark the lunar New Year, though.
On the other end of the country, Hokkaido has a number of sites for the indigenous Ainu peoples, not least the Poroto Kotan at Shiraoi. The "Wajin" presence on the island is reflected in places like Matsumae Castle (the only "traditional-style" Japanese castle on Hokkaido), Goryokaku (the "star fort" built at Hakodate which featured during the Boshin War which heralded the Meiji Restoration), and the city of Sapporo (which was established to be the prefectural capital during the Meiji era).
