Tokyo free kippu allows you to go on any JR trains and subway and sometimes busses within the tokyo met area:
Checkout all the special passes listed halfway down this page:
Transportation in Tokyo
Also if might be worth getting the JR East pass (you can buy it in Japan) if you want to go on daytrips out of the city centre but not as far as say Osaka.
(It even lets you on the shinkansen within certain boundaries if you want)
These will all save you money if you do more than 2train trips a day in my experience, which to get around and see lots of Tokyo, you will be doing, hopping on and off local trains and subways several times a day.