Hallo Peter Andreassen,
That's a very nice plan! You've got 3 good options, depending on where you wish to travel.
The first is the JR Kanto Pass valid in the greater Tokyo area, as well Narita Airport and Nikko. The pass can be a good deal but is limited to 3 days of use.
The 2nd is the JR East Pass this pass covers the complete area north of Tokyo (except for Hokkaido) and is flexible in that it allows you to travel on 5 days within a 14 day period. It is a very good deal if you wish to explore the Tohoku region and is valid on all Shinkansen in the area.
The 3rd is a 7 Day JR Pass this option is the best if you wish to travel all over Japan. It covers all JR lines and allows for unlimited travel trough the country. It would already pay of if you would make a day trip to Kyoto for instance. However it may not be the best choice if you plan to stay locally around Tokyo.
All passes cover the Narita Express to the Airport, which is the most comfortable way to travel to Narita Airport by rail.
I hope this helps!
Daniel