Booking cherry blossom season 25’ late. Looking for recs!

Hi all! So I just found a reasonable flight under $1k trip from sfo to Tokyo for cherry blossom season 3-25-4/11. I’ve read about how things book up WELL in advance (been told last minute bookings are tough)and was able to lock down the first 3 days in Tokyo but still figuring out the rest of the trip. The plan is to hit Osaka, Tokyo, Kyoto, then open to other places. We’re there mainly to see the blooms and trying to book accommodation booked on that (using combination of Airbnb, agoda, Expedia), but I’m very outdoorsy so also looking for any recommendations for outdoors adventures (looking to hike mt Fuji) or sporting events (looks like we’ll be missing the sumo tournaments😢). Does anyone have any suggestions/recommendations for late accommodation bookings, sites off the beaten path(I’ve heard about the cat island and owl cafes, maybe some hot springs somewhere, or a legendary bath house?), and vegetarian/vegan experiences? Also, how much can I realistically see all around Japan in this time frame? Is the language barrier much trickier outside of the big cities? Thanks in advance!