Four years ago when I came to Japan for my first 2-week stay, I spent part of an afternoon in the park in Mitaka. Mitaka is a suburb of Tokyo, and I was there to visit the Studio Ghibli museum. To visit the museum, you buy a ticket at a Lawson convenience store, a ticket with your time reservation printed on it in 24-hour time.
Because I have some difficulty reading numbers, I ended up in the park with about 3 hours to kill. After eating at a Mos Burger down the street and taking a bus back to the downtown area where I drank coffee and ate an eclair in a department store, I'd exhausted every fun activity in Mitaka save going into the Studio Ghibli Museum... and I still had an hour and a half to wait.
I spent the remaining interval- and it seemed more like a day and a half- sketching, taking snapshots and walking around and around on this circular path, while in its grassy center a raggedy group of kids and teenagers played baseball. Some homeless people napped under tarps nestled next to the tennis court fences and some fashionistas in high-heeled black boots sat on benches and discussed Louis Vuitton.
If you want a more detailed and interesting look at what it's like to hang out in a typical Japanese park, you should read "Parklife: You'd Be Amazed" at the Japan Times online site. It's pretty long but well worth your effort. There's even a photo essay that goes along with it you might find fascinating, too.
To me, Japan isn't so much Fujiyama, samurai, geiko, the cyber-madness of Shinjuku, the fashion-crazed youngsters in Harajuku or even the high-powered shopping heaven of Shibuya. It's those things, of course, but it's so much more- or even less. Japan is the work-a-day life of ordinary people, and the un-cool areas they inhabit. Convenience stores, train platforms, office buildings, small houses... and city parks. If you spend 2 weeks in Japan you can see all the wild and weird attractions and feast on the pop culture surface.
But if you live here for a few years, you'll get to know the daily rhythms of real life. And sometimes the beat that accompanies your day comes from the popping joints of old people doing their morning calisthenics in the park, with NHK coming over the loudspeakers.