Since I have lived abroad for a long time, I often get questions like "Do you have any tips for Tokyo visit?"
Here's a collection of such Q&A's.
1 & 6 in this article are my recommendations.
Also, I've heard that people are positive about 3 & 4.
[excursions around Tokyo]
Kamakura & Enoshima Area
1 hr from Tokyo to the South. Close to the coast. Authentic. Perfect walking route in the mountain hopping around the temples. If you take a tram "Enoden" either from JR Fujisawa or JR Kamakura St, getting around along the coast is easy too. Its atmosphere, culture, nature, and food is wonderful. Day-trip is possible from Tokyo, but staying overnight could be nice too. Enoshima is an island that you can access from Enoshima St. of the tram.
Authentic town near Narita Airport.
Authentic town north of Tokyo, 30min by train.
30 min train from Tokyo. Good hiking course. (Actually a serious mountain walk!).
There's a monastery, so you can also enjoy the buddhist cuisine (vegan)
2-3 hrs North of Tokyo. Accessible via train from Tokyo. Deep in a mountain. Big and traditional monastery Nikko Tosyogu. Also easy to find the buddhist cuisine.
2 hrs Southwest of Tokyo. Hot spring area.
Site of Reversible Destiny
The whole park is a wonderful architectural artwork itself. But far from Tokyo.... 3 hrs by train!
NTT ICC (in Tokyo)
Ghibli Museum (in Tokyo)
This is where any Japanese kids would like to go once. Some media art works by Toshio Iwai.