If you're in the mood for tranquility and some fresh air, I would recommend the Institute for Nature Study nature park. It is filled with various plants and trees, flowers and so many birds and bugs.
The closest stations are Meguro and Shiroganedai.
You will be given a guide with names and pictures of bugs to look for. The kids love that.
There are several picnic areas as well. I suggest bringing lunch.
It's free during Golden Week and just a couple hundred yen on normal days.