My tentative 3 week itinerary:

10 nights in Tokyo (will include a day trip to Yokohama for the ramen museum)
2 nights in Osaka
4 nights in Kyoto (might make 1 night in Nara, or can this just be a day trip?)
1 night in Tsumago
2 nights in Hiroshima
2 nights in Fukuoka (either leave from here or back to NRT)

I know that this is weighted pretty heavily towards Tokyo, but I have friends there and some classes lined up so I can't really make that bit shorter.

I'm travelling alone, will be hosteling and my main interest is food! Any suggestions about my itinerary would be much appreciated.

My big question--what sort of rail pass should I get? I'm having a hard time figuring it out. I don't think I need one for the time I am in Tokyo, so should I just get a 14 day one?