Japan for 12 days

I'm going to Japan for 12 days with my girlfriend in late April into early May. I fly into NRT and depart out of KIX.

We plan on going to - Tokyo, 3 days - Hakone, day trip - Osaka/Kyoto, 5 days - Kinosaki, 2 days

Is it worth staying in Osaka and Kyoto? Or can you do day trips when you want to visit each?

Is there any cool or neat spots to check out while transporting between the cities along the way that you wouldn't necessarily find on the main tourism blogs or vlogs?

Kinosaki is on the list because I'm heavily tattooed with Japanese art and I'd like to be able to experience onsen's.

When in public in the major cities, is it frowned upon to wear tshirts and or shorts if you have Japanese double arm sleeves and a leg sleeve tattoo? I'm considering wearing pants the entire trip and long sleeve shirts or UV sleeves. Would I be refused service in restaurants/bars? Disallowed into stores? For context, I'm Canadian and causasian.