First Time in Japan

My husband and I are planing to go to visit Japan for the first time in an eight days vacation starting Mach 15th. This is our itinerary:

Day 1-3: Tokyo
Day 4: Mt. Fuji
Day 5: Kyoto
Day 6: A day trip to Nara
Day 7: Kyoto
Day 8: Tokyo

Do you recommend a JR pass for us since the two of us going to be traveling between cities a lot?

I also heard about a "Seishun 18 Kippu" rail pass that's available in March. Do any of you have experience with that? and what do you recommend?

Thank you so much for the help. I really appreciate it!