The rail pass is worth it if you plan to travel further afield, or use the shinkansen.
I doubt you can use it that much in the tokyo metropoltan area.
A commuter day pass is about 700 yen / £5 and should be all you need in the city.
You may find fares to nearby places are less than the cost of a Rail pass.
http://www.tokyometro.jp/global/en/tick ... icket.html
you can check fares at
http://www.hyperdia.com/
to see if getting a pass is good value
--edit--
The JR pass is only valid on JR trains. Not all train lines are JR. Especially the local services in cities.
Kansai is also easier to travel on non-JR trains depending on where you want to go.
PS it's well worth travelling outside Tokyo.
You can get to Kagoshima in under a day by Shinkansen and limited express ditto Sapporo if you go north. Kyoto is only a few hours away. All your other costs (food, hotels etc.) will be the same, maybe even a bit less.
You don't need a JR Pass for your whole stay. You could start and finish your stay in Tokyo and use a 7 day pass to tour to Kyoto/Nara/Kyoto or further to Hiroshima Nagasaki Kagoshima.
Nor do you have to fly into Tokyo. Centrair in Nagoya is a great airport, KIX near Osaka is also good. then you could use your pass to get to Tokyo for 5 days or so in the middle of your trip.
(booking with Air France via Paris from the UK gets you on JAL for the Paris - Nagoya leg of the journey with really good service)