A month of two you say? Should have no problems seeing most anything you want!
In no order -
Takayama in Gifu : a bit of a train ride, but a very nice old town in the moutains. Some nice museums and easy to get around. Lots of tourist every year.
Kobe in Hyogo : a darn nice city to visit. Very international and quite live-able. Not as overwhelming as Tokyo if you are not a big city kind of person but aside from sites to see, I don't think there is very much you couldn't find in Kobe (one of the two places in Japan I found Dr. Pepper in a standard store - the other being in Tokyo).
Kyoto in, well, Kyoto : Temples and history galore. I recently got back from there and have a few pictures up in the Gallery. Don't have them all up yet though... There is so much on Kyoto I will let any guide book cover that for me and just say it is a great place to visit.
Kurashiki in Okayama (minus Chibori-koen (so says the wife)), Okayama : again, a nice old town and a bit off the beaten path for foreign travelers. Okayama Castle is one of my favorites in Japan.
Kochi Prefecture : Not a town or city like you asked, but it is a great place to travel around. Not the easiest thing to do if you don't speak Japanese or have a lot of time, but Kochi is underdeveloped and thus not totally encased in concrete or devoid of trees (yet). Ashizuri-mizaki, Kochi-city, the Shimanto River, some of the best beaches in Japan, lots of moutains for hiking, and some of the friendliest people I have ever met in Japan.
Haven't made it to Kyushu yet, so just ask NZueda about those sites.
(PS: people might be more game to help if you could tell us what kind of things you are interested in... There are tons of things to see and do in Japan, but it doesn't make a lot of sense to drone on about temples and museums if you really want to spend your time dancing in clubs etc )
Nara: Lots of temples and shrines in a smaller city.
Himeji: Best castle in all of Japan.
Hiroshima: Very lively city. The a-bomb museum can really dampen your spirits, but it is a must see. Nearby Miyajima is rated as having one of the 3 most beautiful views in all Japan. Presumably this was before all the urban sprawl spoiled the mainland, but it is still quite a lovely spot.
Shikoku: Its not a city, but the whole place is nice.