Best value for money

Hi there,
I just wanted to check with you what the best option for me is for my trip.
I land in Tokyo (Haneda) on the 16th of July
4 nights in Tokyo (including probably a day trip to Kamakura - does the rail pass cover this?)
20th July train Tokyo-Osaka
22nd July train Osaka-Kyoto
27th July train Kyoto-Hiroshima
29th July train to Sendai
4th August train to Tokyo
6th August fly from Haneda airport

I was wondering if a 3 week pass is the best option to cover all of this or if a 2 week pass and pay for the extra tickets would be better? (taking into account airport transfers as well) Also would the 3 week pass cover both my airport transfers or would I be one day short?
Thanks for your help,
Hector