From my own kid's (now 8) experiences from when she was 6 & 7
favourite shrine - the Benten-Kutzu cave at Hase-Dera in Kamakura
favourite activity - hiking. We recommend Mt Takao (but avoid the Monkey Park which is just depressing)
loves onsen and rotemburo - there's a good one for a post hike soak at Takasanguchi station
LapGirl liked the Ghibli Museum well enough, but she really loved exploring and climbing through the "houses" at Akebono No Mori much, much more. There's a real fairy tale quality to this place - I'd pour over photos before deciding to go, the area is relatively small and not everyone is going to respond to the buildings in the same way. A wonderful and unique way to experience the Sakura, but somewhere as an adult you'll feel more comfortable visiting whilst in the company of a child.
Showa Kinene Koen - hands down the best park in the Tokyo area. Will keep the adults enchanted and a kid physically engaged all day. Has a range of superb and memorable play areas. Another great place for Sakura. Rent a bicycle. Would be happy to meet up between the 6th and 9th (we're off to Okinawa for snorkelling on the 10th) if you want to come here. My own kid is ridiculously active and very outgoing.
Love of Tottoro? My own favourite spot is the Nihon Minka En. Was so relieved to find out that my kid shares my affection for this very special place.
Also following this vibe is the Ukai Toriyama - a beautiful place for an unforgettable lunch, also near Mt Takao.
favourite museum - Shitamachi Museum in Ueno. The Nihon Minka En gives a glimpse of Country life, the Shitamachi Museum opens up life for ordinary people in the city
We've managed to get close and personal to Sumo Wrestlers near Nihonbashi, but this was October 2016 during a festival. I'm not sure about recommending early Morning Sumo practice - it's early, it's a long session and there's a lot of blood.