7 or 14 day pass?

Hello, My wife and I are coming to Japan on Aug 23rd. We will be in Tokyo from the 23-28th, on the 28th we have a room paid for for 6 nights in Osaka, which is why we are staying for 6 nights, its free. My question is do you experts think we will be ok with a 7 JR pass? My thinking was we activate it the day we leave Tokyo to take the train to Osaka. Once in Osaka we could use it to go visit Kyoto, Nara, Hiroshima, etc and then back all the way to Narita on the 7th day to go home.

Is there any reason to buy a 14 day pass if we plan to be in Tokyo for the first part of our trip? In tokyo we will just be doing site seeing and stuff in and around Tokyo.