If you go during cherry blossom season, you'll want to avoid spring break at TDR.
Here are 2 crowd calendars. Second one is in Japanese (use Google translate).
http://tdrnavi.jp/forecast/disneyland?lang=en
http://www15.plala.or.jp/gcap/disney/
Our first trip, we went during fall foliage and it was lovely. I found it especially beautiful at night the way the trees are lit up.
One of my favorite places is Miyajima (accessible by ferry from near Hiroshima). We stayed one night and I loved seeing the Torii gate at night, plus it gets very quiet and serene after the all the day trippers leave. If you go and it seems oddly familiar, it's because the one at Epcot is based on it.
Near Kyoto, Arashiyama is another of my favorites - really scenic with a bamboo forest. The monkey park is fun too, just don't get too close.
I'm a big fan of the delivery services (Takuhaibin) in Japan. We sent our big luggage from Tokyo to Kyoto and only took backpacks to Hiroshima/Miyajima. It made travelling a lot easier. It's super reliable and inexpensive (think it was less than $30). Just drop it off at your hotel front desk, they'll help you fill out the form and send it off. Also, you should look into flying out of Osaka (the closest airport to Kyoto). If the cost/routing works out, it can save you time and money traveling back to Tokyo.