Thanks everyone for your wonderful advice!
One more question - we are arriving in Narita on May 8th and staying overnight. On May 9th we head to Tokyo where we will stay until the 12th. We have a day trip to Kamakura in there also. Then we head to Kyoto, then Miyajima, and finally back to Tokyo on May 17th. On May 20th we go from Tokyo back to the Narita airport.
Do you suggest the JR rail pass for us and if so, when should we best activate it?