In the Chubu region of Japan, there are three towns with shukubo (temple and shrine stay): Zenkoji, Togakushi, and Minobu.
Zenkoji and Togakushi are located in Nagano and can be reached by Shinkansen from Tokyo. Minobu is in Yamanashi and can be reached by bus from Tokyo (Shinjuku).
There are also many other attractive areas, such as Kanazawa, where you can stay at various temples and shrines.