I would assume the biggest question you have is "How many days is necessary to see a big city like Tokyo?"
Of course you can't see everything, but to get a sampling of the traditional sites plus the neon/craziness/chaos of the city,
Three full days in Tokyo seems sufficient.
For those not used to seeing so many people in one place (We have 13 million people living, just in the central city...), you might want to use your third day to go to quieter places outside Tokyo. The ancient capital of Kamakura, the World Heritage sites of Nikko or the beautiful scenery at Hakone (and hopefully a view of Mount Fuji!) can all be visited as a daytrip from Tokyo.
For those completely lost, I have arranged a rough itinerary so you can see how much you can cover in three days.
And just brief advice on your overall itinerary...
From my experience in the travel agency, I have noticed first-time visitors to Japan spend roughly 7-10 days here, with the second half of the trip centering around Kyoto and the surrounding cities of Nara and Osaka.
With the opening of the Hokuriku Shinkansen (Bullet Trains), Kanazawa is becoming a popular destination now, and I have started to see more visitors making a few days stopover in this city on the Sea of Japan coast before proceeding to Kyoto.
With another few days, the visit could be extended to include Hiroshima and the Miyajima Island.
Most of the international flights to Japan use Narita (NRT) or Haneda (HND) Airport, but there are a few also calling Kansai (KIX) Airport south of Osaka, so it's worth checking to see if your airline has at least a code-share flight involving Kansai Airport.
*Image from https://www.roughguides.com/maps/asia/japan/