Tokyo has 2 airports:
Narita International Airport 成田國際空港 handles the international flights.
Haneda Airport 羽田空港, also known as Tokyo International Airport 東京國際空港, was used mainly as Domestic Airport.
Good News! Haneda opened its international terminal in October 2010.
Haneda (14km away from Tokyo Station) is much closer to the downtown Tokyo than Narita (58km), it takes only 30 minutes to Shinjuku by taxi (much faster if you go to Ginza) …
Faster, but the taxi fare is not cheap …
We took taxi from Haneda to Keio Plaza Hotel (Shinjuku), the meter charge was around 8,000 Yen, but the taxi driver asked for 6,800 Yen only … we didn’t ask why, but happy to have the “discount”.
However, we paid a lot more from hotel to Haneda, the meter was also 8,000 Yen, but finally the bill was 9,250 Yen.
Again, we didn’t ask why … because we believed that Japanese is very honest, probably some surcharge is applied.
For cheaper alternative, you may take Monorail to Hamamatsucho Station which connecting with JR Yamanote Line and the Keihin Tohoku Line.
Or take the airport shuttle bus to major hotel or area.
Many shops and restaurants in Edo Market Place 江戸小路 (before immigration)