N‘EX is the express train connecting Narita airport to the metropolitan Tokyo. Please check its homepage for details. At the Narita airport N'EX station, purchase one way ticket to Tokyo Station, which costs 3020 Yen. At Tokyo Station, change to Marunouchi Line (of Tokyo Metro) to the direction of Ogikubo (not Ikebukuro). You will have to get out of ticket gate of JR at Tokyo Station, and follow the direction to Marunouchi line. You need to purchase one way ticket to Shinjuku-gyoenmae. The hotel is about 200m from the subway station at Shinjuku-gyoenmae. Please check the map around the hotel.