Itinerary help (1st time in Japan)

HI, my husband and I are planning to travel to Japan at the end of October. Any advice/ thoughts on the itinerary I have so far? I’m a bit stuck on day 9-12. We are open to moving things around to make it make sense. Probably doing a day trip to Osaka from Kyoto. Any advice is greatly appreciated.

Also, what’s the best place for shopping?
Specifically for skincare and souvenirs.

We also want to do a onsen for sure but my husband has tattooes. Any recommendations on private onsen?

TIA

Day 1 (TOKYO)
Flight arrives / Head to Hotel / Explore near hotel
Tokyo

Day 2 (TOKYO)
Ueno park, SenoJi Temple

Day 3 (TOKYO)
Mount Fuji day tour

Day 4 (TOKYO)
Meiji Shrine / Takeshita Street / Akihabara / Shibuya crossing / Shibuya Sky (evening)

Day 5 (TOKYO)
Ginza / relax / explore and shop

Day 6 (TOKYO > KYOTO)
Tokyo › Kyoto / check in to hotel / Kyoto Tower / Gyukatsu kyoto / Nishiki market

Day 7 (KYOTO)
KYOTO & NARA tour (Nara deer park, Arashiyama bamboo forest, Togetsukyo bridge, Fushimi Inari)

Day 8 (KYOTO)
Maruyama Park / Gion District / Kiyomizu-dera Temple

Day 9 day trip to OSAKA

Day 10

Day 11

Day 12 (head back to TOKYO?)

Day 13
Breakfast / Check out of hotel / Flight departs
Travel

by martchells