I have a 3 y-o boy, so I hope this would be a help for you!
1) Tokyo Disney land
Despite of it says "Tokyo" but actually it's in Chiba pref which is next to Tokyo.
Takes about 1 hour from the heart of Tokyo.
There are a lot of amazing hotels around Disney land, so you can book in advance to enjoy more or to save your energy and your kids' too.
Sensouji Temple, Tokyo Sky Tree for shopping/ views/ aquarium, Sky Duck bus ride (http://www.skybus.jp/d01.php?lang=en&no=&bno=).
3)Epson Aqua part Shinagawa
I love aquariums and my son loves too.
Especially this one is quite different from the others.
Using lights and various techniques which has innovated by Epson.
I think if you are interested visiting, better to skip Tokyo Sky tree Soramachi's aquarium.
This is the only Lego land in Japan.
If you don't have this in your country or if you do but too far to visit, you can visit here in Japan!
It takes about 1 hour from the heart of Tokyo.
Just right to the next to a big park, so surrounded by trees.
You need booking in advance, but if your kids are bored, you can leave them at park so they can play.
There are a lot of foreign people living around Kichijoji area, so you maybe have some chance to get to know the local foreigners.
They might have more information which will be helpful for your kids.
6) Shouwa Kinen Kouen's illumination for Christmas season
Takes about also 1 hour from the heart of Tokyo, one of the biggest park in Tokyo.
There are so many light-up events in Tokyo, especially around the heart of Tokyo of course.
But sometimes it will be difficult to enjoy it because of your kids.
This park is soooooo huge and not so crowded that you can enjoy much more than Roppongi's ones.
There are some small train rides for kids with the light ups.
The opposite side of the road there's IKEA, and Lala-port ( huge shopping centre) is 10 mins by monorail.
If you could tell me how old they are and what they are intended to interested in, I think I can think something more that will be much more helpful for you!