Should I buy the 7-day pass or the 14-day pass?

Hi everyone!

First time poster here. I am travelling to Japan on the 7th of June - the 22nd of June.

The itinerary is looking as follows:

7th June - 13th June: Staying in Tokyo, generally only travelling around to places like Shinjuku, Shibuya, Harajuku, Roppongi etc. Nowhere really far out.

13th June: Board the Shinkansen and go to Osaka.

13th June - 22nd June: Spending time in Osaka but also travelling to places such as Kyoto, Kobe and Hiroshima.

22nd June: Flying back home at night.

So I was wondering, would it be worth purchasing the 2 week pass and activating it our 2nd or 3rd day in Tokyo that way it covers our trip back from Osaka to Tokyo.

OR

Just buy the 7 day pass, only use it for our time in Osaka, and in order to use the Shinkansen from Tokyo to Osaka initially, buy a separate ticket. For all other travel during Tokyo we'll use the card which you load up money to travel on.

OR..

If you have a better suggestion I'm all ears!

Thanks in advance guys :)