Yoyogi Park is one of the largest parks (and my favorite) in Tokyo. In the spring it is a nice place to view cherry blossom trees and in the fall it is a great place to see some really beautiful ginkgo trees that turn golden. Assuming the weather is nice (and sometimes even when it isn’t) there are plenty of people enjoying outdoor activities, sports, picnics, sunbathing, dancing or just relaxing.
Another interesting thing about Yoyogi Park is that all types of people gather here. If you come on a weekend you will see people playing sports, juggling, playing instruments, dancing and anything else that can be done outside. One of the more unique groups of people is the interest group that is all about the 50s (or maybe 60s). I am not sure if these people dress (and style their hair) like this all the time and are stuck in a time warp or if it is just a weekend activity but you really should take a minute to watch this short video of them dancing.
Yoyogi Park is just minutes from Harajuku Station and is next to Meiji Shrine, so as a photographer you can easily make it a day at these very different (but close) areas. For more information please see the Japan-Guide.com.