Kanto Pass

You can go to all the places except Mt Fuji using a Kanto Area Pass - you could go up to Otsuki and then use a regional pass by Odakyu for the Fuji 5 Lakes Area.

The real issue though is that it is highly unlikely that you would get your money's worth for a Kanto Pass with your plans. It is not made for just going to places in or next to Tokyo. You could use it to go to Nikko, Kusatsu, Izu, Kamakura, and so on and save a ton. Probably regular fare tickets would save you more unless you expand your itinerary.

While the theme parks made for kids are also nice, I hope you will also take time to see the more traditional side of Japan as well.
You could spend a lot of time in Tokyo and still not see everything.
In Tokyo a few of the best places to see are the Tsukiji Fish Market, plus the site that every last tourist goes to see, the Sensoji Temple. If you are in Tokyo on a Sunday afternoon, be sure to go visit Harajuku to see the youth with their wild fashions. Meiji Shrine and Yoyogi Park are next to it and well worth seeing also. And be sure not to miss the Shibuya Hachiko intersection especially on a weekend when it looks like half the city is crossing the street all at once.

I recommend you also try to watch the Japanese people themselves - go to a park and watch the children play. Walk through a supermarket and see what they eat. Living a bit as they do is a great way to learn about their culture - as well as your own.