17 days in Japan

Hi,

We will be travelling to Japan for our honeymoon April 26th-May13th this year. I've planned out a rough itinerary (this is our first time to Japan) but wasnt sure what the best rail pass options would be. We will want to travel around a bit but not too fast paced as we will also be wanting to chill out! Assumed the best approach would be to base ourselves in Kyoto / Tokyo / Osaka and make day trips to places.

I'm assuming a 14day pass would probably work out best.... any advice welcome!

Rough itinerary:

April 26th - May 1st (5 nights) - Arrive Tokyo Narita / a few days exploring Tokyo / day trips to Mt Fuji & Hakone
May 1st - May 7th (6 nights) - Travel to Kyoto / a few days in Kyoto / day trip to Nara? / day trip to Himeji?
May 7th - Spend the night at Mount Koya (recommended by a friend)
May 8th - May 11th- (3 nights) - Travel to Osaka / day trip to Kobe?
May 11th - 13th (2 nights) - Return to Tokyo and blow remaining budget on high end hotel! Fly back to UK.

Many thanks