Narita International Airport: For Shinjuku itself, take the JR Narita Express direct to Shinjuku: roughly 95 minutes and about ¥3,250. It is not the fastest theoretical routing, but it is the sane choice with luggage. The Keisei Skyliner to Nippori, then the JR Yamanote Line, can take 65–80 minutes and costs about ¥2,780, but the Yamanote transfer can be unpleasantly crowded.
Haneda Airport: Take the Keikyu Airport Line to Shinagawa, then JR Yamanote Line to Shinjuku: about 45 minutes, roughly ¥590. It is cheap, frequent and usually better value than an airport limousine bus; buses are convenient for a hotel doorstep but vulnerable to Tokyo traffic.
Tokyo Station: Use the JR Chūō Line Rapid westbound, direct to Shinjuku in about 15 minutes. It is the cleanest central-Tokyo transfer; avoid it with large luggage at weekday rush hour.
Shinagawa Station: Take the JR Yamanote Line via Shibuya to Shinjuku, around 20–25 minutes. It is straightforward but can be packed; this is the useful rail interchange if arriving from the south or changing from Haneda.
Shinjuku Expressway Bus Terminal (Busta Shinjuku): Most long-distance and many airport buses terminate above JR Shinjuku Station. Good for overnight buses and destinations with poor rail links; do not choose an airport bus merely to avoid trains unless your hotel is a short walk away—Narita runs can take around two hours in traffic.