[JohnBraden]

From the States, most flights land at Narita and to a lesser extent, Haneda, so beginning in Osaka will add a domestic flight to your trip for starters. If you're traveling by train to Osaka, it's best to fork over the 28,300 yen for a 7 day JR pass since it would pay for itself on that round trip. You can use the pass on the JR lines in Tokyo: Yamanote, Chuo, etc. You can't use it on the Marunouchi Line and some others.

For food, it would have to be Osaka and shopping, Tokyo....

I don't know if Odaiba is in your itinerary or not, but it has a few attractions, such as Toyota Mega Web (a giant showroom with simulators, etc.), Joypolis (a giant amusement/arcade center), Decks and AquaCity (shopping malls), etc. It's on the man-made island across Rainbow Bridge. If you find yourself spending a rainy day in Tokyo, hop on the Yurikamome line and spend the day there, along with half of Tokyo!