It is the rainy season in June and July, and is extremely hot when the rainy season is over in Tokyo.
I understand you worry about walking a lot under a bad weather.
Here is a plan you can enjoy in Tokyo, when it's raining or too hot.
That is taking a river cruise!
The wellknown place where you can catch a cruise is in Asakusa.
From there you can get to the Hamarikyu garden, Odaiba, and so on.
I would reccomend you to have a glass of freshly brewed beer on board and enjoy the view!