14 or 21 day pass?

Hi there!

We're heading to Japan in October, our itinerary looks like this:

10th: Land Narita Airport
10th - 15th: Tokyo
15th - 16th :Yokohama (one night)
16th - 16th: Mt Fuji (day trip then travel to Kyoto)
16th - 21st: Kyoto
21st - 21st: Nara (day trip then travel to Osaka)
21st - 23rd: Osaka
23rd - 25th: Hiroshima (and hopefully down to
And then back to Tokyo, we leave on the 26th around midday

What would be the best option for travel in terms of single day passes and the 14 and/or 21 day pass?

I was thinking either 21 day pass or a few single day passes (from reading previous questions and answers I assume this can be done in Tokoy?) at the beginning of the trip while in Tokyo and then a 14 day rail pass for the rest.

Any help would be much appreciated.

Thanks!