In your situation, I would just skip Tokyo as you will not have time to really experience it. You can view a modern day Japanese city by spending time in Osaka. Plus Osaka is so much easier to get around for your first time in Japan than Tokyo. It will also wet your appetite for a return trip to Japan. Fly directly into Kansai (the Osaka international airport). Then you can take a round trip Shinkansen trip down to Hiroshima for example for your free day. This is the fastest section of the Nozomi as well. You might try JTB for airfare.
http://www.jtbusa.com/