I don't think it would have been possible to see more than I did given the amount of time I had. Below is an overview of what I saw while I was in Japan over the three main areas I visited (Tokyo, Hakone and Kyoto):
Day 1: Leave from JFK airport direct to Tokyo. Check in at the Shiba Park hotel.
Day 2: Tokyo Sunrise Tour (which included the Tokyo Tower, and a Pearl Factory)