Should we purchase a JR pass?

Hi,

A JR Pass would not pay off for your itinerary. You could get regular rail tickets to make it up to Tokyo or you could fly up on a cheap air ticket on Jet Star or Peach. It's also unclear why you'd spend most of your time seeing Osaka, which is mostly just a clone of Tokyo. Kyoto and Nara are the cultural jewels of Japan and worth most of your time while in the area. Since you are already seeing Tokyo, you can largely skip Osaka during the day. After the temples of Kyoto close down around 5PM, you can zip over to Osaka for the evening. At night the city comes alive and has some great places to see, such as Dotonbori, plus the night views from the Umeda Sky Bldg, and Abeno Harukas Bldg are wonderful.
For Tokyo, if you want to visit Harajuku (plus Meiji Shrine and Yoyogi Park close by), a Sunday afternoon is best if you can, in order to see the youth with their wild fashions.

Good luck!

Mahalo Nui Loa for your response and great suggestions. We really appreciate it and look forward to a wonderful time in Japan!

M4