JRPass 7 or 14 days

Hi!
I am travelling with my wife to Japan. We will arrive to NRT on March 31st. So I am thinking in the following itinerary:

March 31: Tokyo (less than half day)
Apr 1: Tokyo
Apr 2: Tokyo
Apr 3: Kyoto or Osaka
Apr 4: Kyoto or Osaka
Apr 5: Kyoto or Osaka to Nara 1 day trip
Apr 6: Kyoto or Osaka
Apr 7: Hiroshima
Apr 8: Hiroshima
Apr 9: Takayama
Apr 10: Takayama
Apr 11: Hakone
Apr 12: Tokyo
Apr 13: Tokyo (Disney)
Apr 14: Tokyo (departure from NRT)

I know that JR Pass is worth it, but my doubt is: Can I get 7 or 14 days for this itinerary?
I am thinking in activate it on April 3rd. In that case I have to buy single tickets since Takayama. Maybe I can put Hakone after Tokyo (at the beginning) and activate it on 4th. Then I could make the trip from Takayama to Tokyo within 7days. What o you think 7 days or 14?

Thanks in advance.