Is it worth buying a pass for a Tokyo based holiday?

Hello,
My wife and I and our 8 month old daughter are travelling to Tokyo on March 27 for 2 weeks. We are really lucky to be staying with a close friend who is working in Tokyo.
Due to our young daughter we are planning to spend our time in and around Tokyo.
Our itinerary includes visits to Hakone, Yokohama, and Kamakura as well as lots of trips around Tokyo with our friends.
We are flying in and out of Narita. We will be based near Shibuya.
Is it worth us purchasing a rail pass at all? Could we use the passes to get us around Tokyo and would this save us money?
lukeroszko.