Help please!

Hi,
It depends on how much time you are spending in each location. Given the cities you list, a 14 day pass would pay off. But not a 21 day pass, unless the cost differential is covered by the "other cities". Many people might stay in the Tokyo area for the first week and do a number of day trips, then go south and return within 14 days. But you could be rolling down the tracks for the whole 21 days, or do a side trip by flying to Okinawa or Hokkaido and back, etc. The options are numerous.

You need to flesh out your plans more.

Good luck.