Need advise if I should purchase a JR pass

This is my current itinerary:

Day 1-4 : Tokyo
Day 5: Day trip to Hakone then back to Tokyo
Day 6: Day trip to Kawaguchiko then back to Tokyo
Day 7-8: Travel from Tokyo to Kyoto
Day 9: Day trip to Nara and back to Kyoto
Day 10: Day trip to Amanohashidate and back to Kyoto
Day 11 -12: Osaka and back to Tokyo for flight home

Is it best to purchase a JR Pass?