Visiting Tokyo during the New Year period

Planning to visit Tokyo for 10 days, sometime around 21 Dec to 5 Jan, exact dates to be confirmed.

Is it advisable to visit Tokyo during the New Year Period? Will most shops, restaurants etc be closed most of this period or, as some say, these would be closed for 1 day only on 1 Jan in today's modern Japan?

Museum closures are ok as I will not be visiting these.

I intend to visit Yokohama and Mt Fuji on this trip - 1 night stay in Yokohama (seems quite abit to see (and shop) there?). Not sure if I should do a day trip or 1 night stay with Mt Fuji though. Are the chances of a clear Mt Fuji view high during this time?

Would appreciate any advice on the most time efficient and $ economical (for hotel stays especially) routing for my trip.

Also, when does it start to get crowded and busy at Haneda International Airport during this period? I will be catching my flight for home from Haneda International.

Thank you very much in advance for your advices.

The most business places close doors on 28th Dec and reopen on 4th Jan, so 29th Dec and 3rd Jan are the busiest days in Haneda and railway stations.
The most restaurants, bars and cafes are closed on 1st Jan, they operate in short business hours on 31 st Dec and 2nd Jan.
However some restaurants and bars are opened as usual through out years include 1st Jan. I will skip 1st and 2nd Jan and stay inside quietly. All combini stores and tourist places are opened include 1st Jan, no need to buy food in advance. Tokyo Disney Resort is opened 9:00-22:00 on 1st Jan.

Just wanted to add that some stores will be open January 1 ( I was in Shibuya that day this year). The World Trade Center in Hamamatsucho was closed part of the week but did have excellent views of Mt. Fuji when I visited.