A friend planning a trip to Japan had asked me how she might best entertain her children, 2 girls in middle school, while in Tokyo, Kyoto and Hiroshima. (Osaka was also on her list, but I've never been.) She's on my mind today because she is probably in Japan right now... Here were my recommendations, in no particular order:
Take a day trip from Tokyo to Kamakura, and doing the 
trail walk to the Big Buddha (Daibutsu). 
If you like aquariums, visit the 
Tokyo Sea Life Park in Kasai Rinkai Koen (don't know the one in Osaka);
Spend a day at Tokyo DisneySea. Nobody does Disney like the Japanese. The Tokyo 
Disney Resort has two big parks: Disneyland and DisneySea. Go to Sea. 
Less crowded, just as good, if not better. Do not try to go on a weekend
 though. Resort is in Urayasu, Chiba, just outside Tokyo - an easy day 
trip. Take the train to Maihama, then ride the Disney monorail to the 
DisneySea park. (A helpful map can be found 
here.) Don't miss the Indiana Jones ride. Enjoy the people 
watching. 
If
 you're a fan of Miyazaki films (My Neighbor Totoro, Princess Mononoke, 
etc.) you'll love the 
Studio Ghibli Museum in Mitaka, next to Inokashira
 park in 
Kichijoji, a suburb west of Tokyo, I think it's 20 min west of 
Shibuya station on Inokashira line. You'll have to get tickets to Ghibli
 ahead of time, and choose an arrival time on a specific day; maybe ask 
your friend to get the tickets for you, at a kiosk inside any Lawson's 
convenient store in Tokyo. Sounds complicated but it's really not! 
While in Tokyo you could do a spa day with the girls in Odaiba, at 
Oedo Onsen Monogatari, an indoor/outdoor hot springs spa, featuring 
"doctor fish" for your feet. You can have lunch there and load up on 
kitschy souvenirs in between spa treatments. Campy, fun. Also in Odaiba: the 
Sony ExploraScience Museum  
Do you and your girls like cats? Go to a neko cafe! There are quite a few, but I enjoyed two in particular, 
JaLaLa in Akihabara and 
Cha Ma Mo cat room on Meiji-dori near Omotesando-dori.
Also in Tokyo: 
KidZania. It's, um, different. Shy uncertain kids 
will be overwhelmed. Lots going on. Not a lot of English being spoken. 
But kids who are motivated and adventurous seem to get a lot of out it. 
You, however, might get a headache. 
Showa Kinen park - a great big amazing place just outside Tokyo, 
west of Shinjuku. Enter at Nishi Tachikawa gate for easier access to the
 best parts: Rainbow Hammocks, Bouncing domes, Dragon Dunes, Misty 
Forest, Bonsai garden. Grab an English map when you get there. 
This one 
doesn't point out everything.
Need a zoo? the Ueno park zoo has pandas again, but Japanese zoos in general are depressing - big animals in tiny spaces, etc. The Tama zoo west of the city is an exception, I think. If you go, be sure to ride the 
Lion Bus.
While in Kyoto, don't miss the Fushimi Inari shrine, on Mt. Inari, 
just outside the city. A nice trek through some 10,000 torii gates, lots
 of statues of foxes (representing Inari, a fox deity, Shinto god of 
rice, I think). One of the local train lines takes you right to it. View this 
slideshow of pics or read the rave reviews posted on 
Tripadvisor.
Also from Kyoto, you could spend a day in 
Arashiyama (bamboo forest,
 monkey park) and/or a day in Nara, where at the famous temple Toda-ji, 
the kids can crawl through Buddha's nose for enlightenment. 
While in Hiroshima, take a commuter ferry out to 
Miyajima island, if the weather is good. There's a famous 
big red torii - try to be there to see it during both high and low tide.
Almost forgot - the 
Hakone Open-Air Museum! It's terrific. One big
 sprawling sculpture garden. Climbing ropes for the kids inside the 
"castle of nets." A foot bath at the end, to soak your tired feet. This is a day or overnight trip from Tokyo. A few other things to do in Hakone (there's lots) mentioned in the Tokyo city guide 
side trips piece I wrote awhile back.