I like gates_2's suggestions, and if you want a bit more of a look at rural Japan, a day trip to Nikko is an option.

I've been to Hiroshima, and in fact, I'm going again for a conference at the end of this month. However, unless you are very interested in the atomic bombing, there's not much else there for the first-time visitor, other than Miyajima. This is especially true since the castle at Himeji, otherwise a great midtrip stopover, is being repaired and is reportedly covered over during the process.

In fact, if you travel mostly on the Shinkansen, you'll be in cities and suburbs for most of your trip, because that coastal strip is where most of Japan's population is concentrated.

For a short trip, I'd recommend two bases: Tokyo and Kyoto, with day trips from each. Each city has enough to keep you busy even without day trips.

Guidebooks are available for both cities from several publishers, and the guidebooks include suggestions for day trips.