Narita Airport to Sengakuji Station - summary
The Keisei trains that run directly from Narita Airport to Sengakuji Station (which is very close to Shinagawa and a convenient station to arrive from if then taking a taxi towards Azabu Juban or Roppongi - in fact the money saved by not using the NEX will cover the connecting taxi fare if there are two or three people travelling together) seem to be quite frequent throughout the day right up until 18:07 Narita T2, 18:04 for T1, with up to two trains an hour.
Unfortunately, after the 18:04/07 departure the rest of the trains (which also run throughout the day) involve a simple platform cross change at Aoto or Keisei-Takasago as jib71 has described. There is one final exception which is the 23:00/02 departure which goes to Sengakuji directly.
The adult fare for these direct trains is 1,380yen and journey takes roughly 75 minutes. (As a comparison; from NRT to Shinagawa by NEX is 3,190yen and usually takes about 65 minutes)