There is no direct bus from Narita Airport to Shinkubo Station; You can take Limujin bus (3 100 yen) to Shinjuku outside the arrival hall of the airport and get off in front of Hilton Hotel. It is less than 2km from Shinkubo Station, so you can take a taxi there (730-890 yen, depending on the route).

T 1 Terminal 1 Bus Terminal Outside the Building

It's cheaper to take JR train. Take the airport express train (dark blue) at the second terminal and get off at Rimali Station. Walk in the direction indicated by the sign at the top of the station for 6 minutes, take the Yamanote Line (light green) to Ikebukuro/Shinjuku at Rimuri Station, and get off at Shinokubo Station after 9 stops. The journey takes about 65 minutes and the fare is 2650 yen.

After getting off at the station on the left, follow the signs to the east, climb the stairs, cross the railway, and get on at Rimali Station on the right.