I have already told you about green lungs accessible in Tokyo, the huge concrete city, including Shinjuku Gyoen gardens and Yoyogi Park. Meiji-jingu is just adjacent to Yoyogi and a must-see during your visit of Tokyo.
This is actually a huge Shinto complex, first via the walk in the imperial garden (Meiji Jingû Gyoen) that leads to it, and after passing under the first big Torii. Then the tour continues through a hundred thousand trees forest, up to the courtyard that hosts several traditional weddings every weekend. You can follow this visit in my pictures a little lower on this page.
Contrary to what you might imagine, the construction of Meiji-jingu goes back only from the early 20th century. It was built in honor of Emperor Meiji and Empress Shoken. Today, the shrine is visited especially for the New Year festivities, during which a average of 3 million Japanese come pray.
If you plan to visit Meiji-jingu, stop at Harajuku subway / train station and go uphill to Yoyogi, but beware: it closes its doors at 4:30pm (and even 4:00 p.m. between November and February), and the last entry is is a half an hour before that!