1) From Tokyo, should I go Hakone or Mount Fuji first? If I only want to allocate one night, should I spend the night at Mount Fuji or Hakone?
2) Is it worth to stay at a night at one of the Disney hotels to cut travelling time to visit a=land and sea?
1. For me, I would stay at Hakone. Can also see Mt Fuji from some parts of Hakone.
As mentioned, Hakone area consists of many hot spring type resorts.
If that isn't your thing, then don't need to go to Hakone.
As for Mt Fuji, I'm not sure what u really want to do there.
As for climbing up the mountain or staying close to the base of Mt Fuji, maybe someone else knowledgeable can help!
2. If u are going to both parks, would be nice to stay at one of the hotels there.
Some hotels there have disney themed rooms.
Save time n money on travel n u can see the fireworks too if room faces the parks.
If room faces tokyo bay, can sometimes see Mt Fuji as well.
There are also airport buses that run straight from airport to the hotels in the disneyland area.
So if u plan to stay at one of the Disney hotels, can consider staying on the 1st day of arrival or last day before departure.
Pls check to see if they are available before booking.
I think if u stay in one of the main Disney hotels, might be able to get early entry...not fully sure on this.
I stayed at Hilton in the disney area. Not one of the main disney hotels but they had disney themed rooms n very close to the parks.
The room also faced tokyo bay n could see Mt Fuji in the morning before clouds covered it up.