We took our 3 year old to Japan and had a difficult time entertaining them with our usual cop-out: playgrounds. Japanese public playgrounds are few and far between, and when we did find them they were typically old and sad (a swing or monkey bars and a metal slide). The swings we found were abnormally low to the ground, making it difficult for kids to actually pump their legs and most end up standing on them instead. We did some research into it, wondering if Japanese people felt as frustrated as we were trying to physicslly entertain a kid.

We came across this interesting piece about physical differences between kids in 2007 and kids in 1985. In short, the average 5 year old in 2007 had the athletic abilities of a 3 year old in 1985. Granted this data is rather old, but anecdotally we did notice our 3 year old playing on equipment specified for (and mostly being used by) the much older children. https://poh.ngo/en/the-state-of-play-in-japan/

The best public and highly used playgrounds we found were in Kyoto (near the train museum), in Osaka called the mountain slides (near the Children's Plaza), and in Arashiyama at the top of the Monkey Park hill. Aside from that, paid entertainment was the way to go.

Happy to share more if anyone is interested in the experience, but I'd rather stop there for now.