On weekends, I wake up and feed my daughter, quietly lay her down next to her sleeping father, and escape for a jog in the park. Neither one realizes I've left the house. I love this time to myself!
Parks are the most awesome places in the morning on weekends. Besides the usual joggers and dog-walkers (big, naked dogs, unlike the decorated datsuns and chihauhaus you see all over Tokyo), a lot of people are out doing calisthenics of all sorts. No matter what time I go between 7 and 9 a.m., I always see two separate Tai Chi groups, one of which exercises to music. Today I also ran past a little old lady walking fast--and backwards--along the path.
If you're near a big park in Japan, head there on some weekend morning and report what you see!