In Tokyo, the Asakusa Kanon Temple and Meiji Shrine are must sees. When I was in Tokyo, I visited the Meiji Shrine on the Emperor's birthday and witnessed a great Shinto dance by some shrine maidens!

Beijing, great choice. It will be cold, really cold during January. It's a dry coldness so be ready. Recommendations: YongHeGong Lama Temple. This temple is quite nice and it is in the middle of the city. In terms of spirituality if you are looking for something a bit more off the beaten path then head to TanZheSi. This place, though, is to the west from the city. About one hour on subway and then another 40 minutes to get there by bus or taxi. It is quite nice and not many people go there. This temple is much older than the city. Aside from these stops there aren't many spiritual places in Beijing.
In Tokyo city Asakusa is nice, but it is flooded with tourist from Japan and from abroad. It is still nice to see though because some people really are worshiping. A place I would suggest would be Narita Shrine. This place is two subway stops from Narita Airport. It is really big and it's really spiritual. Many people visit this place, but it is so big that you don't really feal it. Most of the structures are made out of wood. The temples are not painted, neither are the wooden carvings. This place is special.

good day,

Armando