Which JR Pass should I opt for?

Hi there!

I am currently planning for my trip to Japan this May. I will be flying to and back from Tokyo, and it's a 11-day trip.

I'm thinking of covering the following cities:
- Osaka (3 days) - Kyoto (2 days) - Nara (1/2 day) - Kobe (1/2 day) - am still deciding if I should go for the 2 x 1/2 day trips - Nagoya (2 days) for theme park and flower park - Hakone (1 or 2 days) for Mt Fuji - remaining days in Tokyo

Do you think this is being too ambitious?
And should I opt for the 7-day or 14-day JR pass?

Kindly advise.
Thank you!