[princessmarisa]

It depends where you can fly into but I'd say

Hiroshima - Osaka -[Kyoto - may not need to stay here you can jus get daytrips from Osaka]- Nagoya - Tokyo - Sendai

is just about doable in a Month.
I am not sure if Hokkaido would fit in the end without cramping the rest up and also spending a lot of time and money travelling.

Do not miss doing a sidetrip to Miyajima from Hiroshima.

Other nice things off the top of my head are arashiyama from Kyoto/Osaka.
Maybe a trip to Kobe from Osaka region too.

I think there are a lot more places you can get to as side trips from Osaka than from Tokyo so I would book the longest part of your trip to stay there.

I didn't think much of Nagoya or Sendai but we didn't really plan what to do when we got there so that is probably why. We also went as far north as Niigata and again , didn't plan it well so found nothing of interest there.

Get your big plan down then you can start filling in the details of interesting places to see form each of the main bases.