Hi there!
As a JR Pass cost the same as a return trip ticket from Tokyo to Osaka, then I can certainly recommend you use the JR Pass. I recommend the following approach:
- Purchase a Narita Express + SUICA card single deal on arrival in Japan. This will get you into Tokyo and will also give you ¥1500 of travel value on the non-JR Tokyo Metro that you will certainly use a little while you are in Japan.
- Activate your 7 day JR Pass on day 2 for your travel down to Osaka. This will cover all your travel up to your departure on the 4th, including the trip back to the airport.
With this combination you will find you have very little travel problems and will strike a good balance between saving money and convenience.
July and August are not particularly busy (actually, March and April are one of the peak seasons in Japan!), but you will find it very hot in these summer months.
As you are travelling with family, and are also on the Tokaido line, I do not recommend the Green Pass. I think you'll get better value for money from a standard class pass.
Hope this helps!
