Fun for Kids & Families to enjoy all over Japan
Of course there are amusement parks, including Disneyland and Universal Studios in Japan; fun playgrounds and adventure parks too. But I think even the day to day can offer fun experiences for kids.
Kaiten-sushi (sushi train) shops are lots of fun, soba and udon noodle shops, buffet dining and retro burger shops are great places to eat out with kids. For snacks, kids here eat lots of rice balls and quite healthy snack options from any convenience store.
Festivals offer not only fun foods to try from stalls but also color and culture to take in. Firework festivals seem particularly fun for all the family- although the crowds are never very fun with kids - choose a spot where you can see the fireworks, from a nearby riverbank perhaps, but not in the midst of the crowds with kids.
Festivals around Japan: http://en.japantourist.jp/index/search?q=festivals
Hiroshima's flower festival is great spectating- fun costumes and and dances. You can see similar "flower festivals" and "Yosakoi parades" like this in other areas of Japan: http://www.youtube.com/watch?v=v4Pp2unWRG8
Museums of all sorts from art to history to film and manga libraries offer interest for kids.
Parks, amusement parks, beaches, rivers, forest walks, camping, rental bicycles and of course the zoos.
Japanese castles often offer chances to meet warriors in costume or to dress up yourself. Temples and shrines have interesting amulets and customs that include kids.
Kid-friendly places around Japan:
parks, recreation and place reviews all over Japan:
Family fun around Japan: