9 day itinerary help

Hello, my family of 4 is going to be in Tokyo/Osaka Japan for 9 days 8 nights.

We have what many of you may consider a loose itinerary based on what else i have seen while hunting the threads for ideas, I don’t want to over plan but I don’t want to underestimate our ability to get the most adventure out of each spot. This is my families first adventure abroad.

Day 1
Arrive around 4:30p at Narita, private transfer to Taito City Tokyo and explore by foot for a late dinner spot near by

Day 2
Tokyo Day, must sees are Tokyo Tower all the way to top, Imperial
palace and grounds, and Meiji Jingu. Are the zoological gardens nice? Open to recommendations
Hoping to go to a nice dinner.
Same hotel for overnight

Day 3

Wake up, slightly more exploration by foot, board Shinkansen to Osaka between 10-11:30

Arrive in Osaka, make our way to dotonburri (hotel is here) and explore before walking the streets, open to recommendations for a beef and sashimi dinner experience or a walking food tour

Day 4

Osaka/Nara exploring with Kinkakuji, Osaka Castle, 1/2 cycle tour and maybe a sumo lunch experience or a bay cruise
Baseball game in the evening (tix purchased, our must do for the trip)

Day 5

Kyoto tour, imperial palace, bamboo forest (haven’t reserved yet, so open to recs)

Day 6
Morning tea ceremony?
Make our way back to Tokyo
Can we visit a warm springs in the way? Leaving this day open to exploring something that a local or other traveler suggests.
Staying in Koto City area of Tokyo

Day 7
Mt Fuji and lake day trip return to Tokyo

Day 8

Day in Tokyo, not sure what to do, will check things off our list if we haven’t done them like tea ceremony, sumo lunch…

Day 9

Slowly make way to Narita, buy souvenirs, last minute food experiences, flight departs at 6 PM.

Do I need to add more structure to get more bang for our buck? I know there’s a million things we won’t see on a trip this short, but am I overlooking anything ?

Thank you! This has been a very helpful forum so far.