During my travels throughout Japan I’ve noticed a lot of places and entertainment options geared towards children, and I think families would really enjoy them.
Theme parks
There are many theme parks for kids in Japan, such as Tokyo One Piece Tower, Tokyo Disneyland, Tokyo Disney Sea, Edo Wonderland in Nikko, Sanrio Puroland, and many, many more.
Aquariums and zoos
Alongside watching a great variety of the ocean inhabitants, many of Japan's aquariums offer interactive options! Visitors are able to touch penguins and fish at Miyajima Aquarium, feed birds and penguins at the Kobe Animal Kingdom, and so on. Every aquarium provides unique experiences and entertainment for kids.
Museums
There are special museums such as the famous Ghibli Studio Museum, which is very interesting for both the young and young-at heart, the Anpanman Museum and Mall in Sendai, and the Yokohama Doll Museum. Various Kokeshi museums in the Tohoku Region provide classes for children where they can paint their own kokeshi dolls.
Amusement parks and attractions
In Tokyo you can find places such as Hanayashiki Amusement Park in Asakusa and Tokyo Dome City, and at Ueno Park kids can enjoy sailing on swan boats. Cosmo World in Yokohama features attractions for kids of any age. In Hakone, children can enjoy a ‘pirate’ sailing ship across Lake Ashinoko.
Shops
To my surprise, I didn’t see too many children's shops in Japan. Some that I did spot and bought gifts at were Hakuhinkan Toy Park in Ginza, the observation deck of Tokyo Metropolitan Government Building, Disney shops in Shibuya and Sendai, and some independent shops at Venus Fort in Odaiba and in Yokohama.
Children's Festivals
In Japan there are three special festivals for kids. The Girls Festival is known as Hina Matsuri, and is celebrated on March 3, but about a month ahead there are numerous special doll displays across the country. The Boys Festival Kodomo no Hi is celebrated on May 5, but also about a month ahead there are displays for boys including models of samurai armor and carp streamers hung everywhere. Lastly, the Children's Festival ‘Shichi-Go-San’ (Seven-Five-Three) is celebrated in November, and children of those ages have ceremonies in Shinto shrines all over Japan.
Of course, this is not an exhaustive list of things to do with kids in Japan, but it may encourage traveling here with your family!
The Doll Museum in Iwatsuki doll town is fascinating.
https://en.japantravel.com/saitama/iwatsuki-doll-history-museum/41516