3 major airports in Japan, Narita International Airport, Haneda Airport, and Kansai International Airport, have the offices that you can activate your Japan Rail Pass.
Therefore, you can use Japan Rail Pass to go to city central from the airport.
Narita International Airport is located in Narita city of Chiba prefecture, far from Tokyo central. It takes at least 60 minutes by shuttle from the airport to the city central. And, it often take longer due to traffic jam.
By train, you can avoid delay of arrival as most of trains are on time.
One popular train from/to Narita International Airport is Narita Express (N'EX).
Narita Express (N'EX) is a limited express train operated by JR from Narita International Airport to Tokyo, Shinagawa, Yokohama, Shibuya, Shinjuku, and Ikebukuro.
This express train is the only train going to Shibuya, Shinjuku, Ikebukuro, Omiya, and Yokohama without transit. Therefore, it is very convenient if you go to those areas.
You can use your Japan Rail Pass to take Narita Express if you activate your pass at the airport.
Tokyo Monorail is linked to Haneda Airport International Passenger Terminal. You can take Tokyo Monorail to Hamamatsucho, then transfer to JR lines (going to Tokyo, Shibuya, Ueno, Akihabara, and Ikebukuro) or subways (going to Roppongi, Ginza, and other subway stations in Tokyo central).
Tokyo Monorail station is linked to the International Passenger Terminal of Haneda Airport. You can be at Tokyo central within 30 minutes by Tokyo Monorail. This is recommended transportation from Haneda Airport to Tokyo central.
You, of course, can use your Japan Rail Pass for Tokyo Monorail.
Kansai International Airport has a JR station, Kansai Airport. Therefore, there are JR trains from/to Kansai International Airport.
Haruka is a limited express train operating between Kansai International Airport and Maibara. You can take this express train from Kansai International Airport to Tennoji, Shin-Osaka, Kyoto, Omihachiman, Maibara, and more.
It is a popular way to go to Osaka city central and Kyoto from the airpot.
Since there is the office where you can activate your Japan Rail Pass at Kansai International Airport, you can take limited express Haruka with your Japan Rail Pass.