Planning Train Itinerary

I am travelling with one other adult to Japan in June for 14 days, and trying to figure out the most cost-effective travel strategy. Here's our rough itinerary:

Day 1: Land in NRT and travel to Tokyo, staying in Ueno.
Days 2-5: Staying in Ueno and traveling to other Tokyo neighborhoods.
Day 6: Travel to Hakone ryokan.
Day 7: No travel.
Day 8: Travel from Hakone to Kyoto.
Days 9-11: Staying in Kyoto and travelling between districts. Possibly a day in Miyajima.
Day 12: Kyoto to Nara.
Day 13: Nara to Tokyo.
Day 14: Tokyo to Airport.

Is a 7-day pass the most effective, or 14? If we get a 7-day pass, when should we use it?

Also, does this itinerary seem balanced?

Thank you in advance!