Hi!
Like the others said, radiation is really not something you should worry about.
If this is such a big concern, then stay away from Fukushima and maybe Miyagi Prefectures.
A pretty standard route for first-timers is: Tokyo-Kyoto(Osaka)-Hiroshima
Like Glenski said, it really depends on many things, though.
What are you interested in the most? How long will you stay in Japan?
Some areas in Japan get a lot of snow in winter and it might be difficult to travel around, other areas are BEST to be visited in winter, so I'd like to suggest a few things:
Shirakawa-go is stunning in winter!
The snow monkeys in Nagano are a must-see while they're bathing in a hot spa in the snowy mountains!
Visiting an onsen resort such as Kusatsu in Gunma might be a nice idea, too, but it really depends on how much time you have.
If you're interested in
Ninja, then I recommend Iga-Ueno to you.