Getting from and to Narita
Transportation around Tokyo is currently running a reduced service. Here is our current advice on getting from and to Narita airport. Please note that this is a guide and may change at any time. If you are running to a schedule, please allow extra time to reach your destination as all routes are likely to be congested.
The following rail lines were running a reduced service from and to Narita on the afternoon of the 15th:
NOTE: The NEX (Narita Express) is currently suspended.
There is a limousine bus service that goes from/to Narita and departs from many stops in Tokyo. Please note that the bus service costs around ¥3000 pp and will take around 2 hours. The bus service is also likely to be running a reduced service too, and is generally busy so please ask at the bus counter in Narita or ask your hotel to call on your behalf.
Google translated limousine bus status page. Please note that seats are full for the 16th. Booking for seats on the 17th will open via telephone(03-3665-7220) and online booking on the morning of the 16th at 9am JST.
Taxi costs will depend on your zone in Tokyo, but are in the range of ¥19,000 - ¥22,000. You can find a list of prices here: http://www.narita-airport.jp/en/access/bus/detail_taxi.html. If you do travel by taxi, we reccomend you travel in a group to reduce costs of travel.
Phrase card for Bus and Taxi
Japan Rail Pass - JR Exchange Order Offices
thanks to @Rute for some information