21 day rail pass

Hi all. Would like confirmation that a 21 days pass is best. Itinerary as follows:
Arrive Narita 7 Oct - sight seeing Tokyo and area, staying Shinjuku x 3 nights*
Depart Tokyo 10 Oct for Utsunomiya x 3 nights
Depart Utsunomiya 13 Oct for Takeyama for 2 x nights
Depart Takeyama 15 October for Kanazawa x 2 nights
Depart Kanazawa 17 October for Kyoto x 4 nights
Depart Kyoto 21 October for Nagasaki x 3 nights
Depart Nagasaki 24 October for Osaka x 3 nights
Depart Osaka 27 October for Kansai airport.
* Figure we could activate our JR rail pass on arrival at Narita and catch NEX into Shinjku?

Look forward to comments and any suggestions will be welcome as to travel advice, sightseeing must do's, etc.

Kim