Tokyo is cool and all, but after a few times (7 or so) being there, it's usually my fly in destination, before I gtfo. Since this is your first time, you should be able to find enough to do in Tokyo. I would just watch YouTube videos, search something like 7 day Tokyo itinerary and see what looks cool. I know I am missing a ton of shit, but just some stuff that stands out after many years of not being there. Tokyo Tower, SkyTree, Imperial Palace Gardens, Asakusa area, Akihabara, Ueno park, Odaiba. I don't even recall anymore. Thinks I thought were cool back then not so cool to me anymore as I get older. I can't really imagine Tokyo as a family vacation, seems weird to me. It's like going into a city of 14 million people and then trying to find something to do as a family...much rather enjoy it by myself. Some of the theme parks and stuff might be cool, but I never went to those, never was my thing, but if you are into that, then as others have said, book in advance. It's a cool place for sure, just not the place I would pick for a family vacation personally. If you can, try to find flights into Haneda, it's a stone throw away from Tokyo, vs Narita, which is an hour away by train.
As others have said, Japan Rail pass was a good option at once, not so much anymore as they nearly doubled the price. Before a round trip from Tokyo to Osaka would be a breaking point on a 7 day pass, now it's two trips, and hardly worth it. When I first went to Japan, I was there for 7 days and did Tokyo/Osaka/Kyoto/Hiroshima and back to Tokyo in a week, putting the pass to good use. If you just want to hit up important places on your first visit, it's a good way to go, but not sure if it makes sense with family.
Enjoy the trip. I'm off to Japan again in 40 days myself for 3 weeks, haven't been back since my canceled trip in 2020...fking covid. If you want to see cherry blossoms, end of March and beginning of April are your best times. I have been there during those times 4 times myself, and it's always beautiful. They open at different times throughout the country, so if you don't get to see them in one spot, you may in another part of the country if you willing to take the bullet train.