If you're arriving in Japan via Narita Airport and spending at least two full days running around Tokyo, I recommend that you get Suica & N'EX.
It's a commuter package made available exclusively for foreign passport holders. With it, you get two train tickets: a stored value subway pass (Suica card) and a seat reservation on board the Narita Express (N'EX).
N'EX is a great time-saver. It gets you into metropolitan Tokyo quickly enough. One hour to Tokyo Station, another twenty minutes to Shinjuku Station.
Price-wise you do save though not as much as its website strongly suggests that you do. You save on the N'EX itself. But there are cheaper trains running to and from Narita Airport too.
¥1,000, 75 min – Keisei Limited Express to Ueno Station
¥1,300, 85 min – JR Sobu Line to Tokyo Station
Note that transfers from one line to another inside a station can sometimes mean a long walk. Check out Hyperdia-timetable. It'll tell you how long it takes to get from one station to another, factoring in the estimated time it takes to hike from one line to another.