I haven't been to Tohoku much so can't help you there. Here is a list of interesting places:

Kanazawa/Noto Hanto
The famous Kenrokoen is located here. Famous for crab but really should be visited in the winter time. Wakura Onsen further up by the bay has many onsen ryokans.

Okayama/Kurashiki/Himeiji
The other famous garden Korakoen is at Okayama and this is a summer garden. Kurashiki has a historical canal area. The Himeiji Castle is not to be missed. The Okayama ekiben (station bento) is famous.

Matsuyama
Famous for the Dogo Onsen. Doing the shrine walking tour on Shikoku is too much but visit a few should be interesting.

Kumamoto
The Kumamoto Castle is where the last samurai revolt occured in 1877 and the movie Last Samurai is loosely based on this event. It is also where the famous swordsman Miyamoto Musashi lived. They have quite a few onsen there and the live volcano Aso San is close by. It is famous for basashi (horse meat), renkon (lotus root) and shoju made from sweet potato.

Shimane/Masuda
This is a seaside town way out west on Honshu. It is famous for ika sashimi and they eat the ink too. Tsuwano close by has preserved residences also. The Ryokan in Masuda is relatively low cost.

Mito
This is where Tokugawa Shogun set up his youngest son after securing Japan. Since he was not expect to do much fighting, this daimyo worked on education and built the Kairakoen (one of the 3 famous gardens). Since it is famous for plum, should be visited in Feb/Mar time frame. Food is everything plum, natto and ume shu (plum wine).

Nikko
Many references on the web.

Misaki
A day trip from Yokohama other than Kamakura, Enoshima area will be to take the Keikyu Line to the end and take the bus to Misaki. The Misakiya has an all tuna lunch that is pretty interesting. Take an upstairs tatami room and watch the activities below in the harbor.

Have fun.