Ride #97 TOKYO CITY BUS for sightseeing
It takes about 20 minutes by JR from Shinjuku to Shinagawa, but about 1 hour by Shinagawa 97 from the West Exit No. 1 bus stop.
It will be a bus trip through Shinjuku 3-chome, Gaien Higashi-dori between the National Stadium and Akasaka Imperial Palace, Aoyama 1-chome, Nishi-Azabu, Hiroo, Shirokane Takanawa, and Sengakuji.
There are about 3 trains per hour, so you can enjoy sightseeing while getting off the train with a 500 yen one-day ticket.