Tokyo>Osaka>Tokyo

Hi,

I will be going over to Tokyo and Osaka for 9 days and I am really unsure of which JR Pass should I get. My itinerary is as follows:

Day 1 : Arrival at Haneda Airport, walking around Shinbuya
Day 2 : Harajuku station, Shinjuku area
Day 3 : Mt. Fuji
Day 4 : Tokyo tower, Tokyo Dome, Akasaka
Day 5 : Going to Osaka
Day 6 : Shopping around Dotonburi, Namba
Day 7 :USJ
Day 8 : Osaka castle, Nara Todaiji Temple
Day 9 : Back to Tokyo, Narita airport.

I am thinking of purchasing a JR Pass for my 3rd to 9th day of my trip.

My questions are:
-are there any major issues with my itinerary? -Which JR Pass should I buy for my trip? -would the JR Pass have complete unlimited rides along all the JR Lines for both Tokyo and Osaka?

Thanks for the help! I am really confused and clueless about these issues. Your response is greatly appreciated! :)