Hi Hubert,
Osaka is a very nice city to visit, the local atmosphere is something you can't find anywhere else in Japan. There are basically two main areas in Osaka. The more uptown Umeda district, here you'll also find Osaka station and the more downtown Namba area. Especially Namba is very lively, here you'll also find the closely Dotonbori and shopping streets of Shinsai Bashi. I definitely recommend walking around in this area, here you'll also find many local delicacies to try.
Nagoya is more of a business town and does not offer as much for tourists as other bigger cities do. Its good for Shopping. If you do want to visit it, then I recommend looking at specific places/sightseeing points ahead of time and visit those.The train museum in Nagoya is very nice.
Fuji, please have a look at this page for all the details.
Hope this helps,
Daniel