Local schools can vary like everywhere, but the Japanese ones are generally good environments for kids. I've taught in 4 (senior and junior high both academic and engineering/sports in Kanagawa and rural Japan) and the school community is insanely strong, with club activities, competitions and festivals making them like a second home to the kids and teachers. The learning system is quite intensive and often focused on memorisation with a somewhat inflexible approach, but that suits some children (although in Tokyo there is more flexibility depending on the school compared to rural Japan). The biggest thing you will have to get used to is the presence of school in your and your child's life. They will have shed-loads of homework as they are expected to prepare before each class. The club activities are also very intense compared to most places, (be they sports, art, brass band, choir, chess or engineering etc) and are attended pretty much every day if not twice a day for sports (including throughout holidays and Christmas day etc - get used to that). This all sounds kind of bad, but honestly, they build such strong relationships and learn the importance of teamwork, responsibility, respect, dedication and focus they are some of the most well rounded kids I've ever met (they not only become very skilled at certain things, but listening to their speeches about their experiences made me realise how much they love this life). Be prepared to know your teachers well too, they do home visits and your homeroom teacher will consider themselves highly responsible for all their students, almost like a third parent.
I've had students at Junior high join from abroad and become practically fluent attending regular classes within months, as they go for full immersion. You'll want to discuss this with the school though as some are definitely better prepared than others. Kids can be mean like anywhere, but generally the behaviour here is far better than at home (UK).
What you may what to consider most is the high-school they attend as this is where the system divides into specialist schools, with academic, engineering etc becoming the focus. Many schools have a language stream and students from these high school often go on to attend University abroad, which might be a good idea for your kids. There are no standardised tests in Japanese schools, so they will sit exams for each high school they attend, often with say, a focused English exam if they apply to a language-stream school.
I would say go for it. It's the best way for you and your kids to become part of the community, especially if you plan to stay here. If it doesn't work for them after a while then fair enough, at least you tried. I am biased though haha, so it would be interesting to hear from the other side.