In my article ‘Osaka for kids’, I recommended visiting Nara rather than Kyoto when you have kids in tow. Here are the reasons why.
Visiting Kyoto, the old capital of Japan is a must for tourists. However, you might get ‘temples and shrines fatigue’ after visiting so many, especially when you don’t appreciate those things in the first place. My mother-in-law once said, “Visiting one old church a day is enough.” Your kids will be less likely to be impressed with ancient buildings that look similar to their eyes.
Nara is the oldest capital in Japan, and is easily accessed from Osaka. Or if you like, you can take a train from Kyoto. Unlike Kyoto, the area of main attractions is fairly compact. Nara Park has Todaiji Temple with the huge Buddha statue, and many deer roaming around.
When you look up at the huge Buddha, pay attention to his nostrils. A hole of the same size is in one of the pillars. Kids can go through it. (I advise you check the size carefully before you try.) Once you are outside in the park, buy a pack of biscuits for deer. (10 sheets for ￥150.) Warn your kids that some deer are aggressive, and of course, tell them the biscuits are for the deer only, though harmless for humans.
In short, Nara is a theme park with fun activities. I enjoyed them as a kid. You can picnic in the vast grassy field, or if your kids are happy to see more cultural heritages, visit Kasuga Shrine and the museum, or further afield to see other famous temples.