Southern Terrace
The promenade next to the Southern Terrace exit offers a magnificent view of the Takashimaya department store and a bridge that offers the best views for watching the trains enter and exit.
Tokyo Opera City
A skyscraper with a shopping center and art museum that often has interesting multimedia exhibits.
Shinjuku Gyoen National Garden
A large public garden, and one of the most popular places for viewing cherry blossoms in the spring. It has Japanese, English, and French gardens, as well as Taiwanese teahouse and a botanical conservatory. The entrance fee often makes the park surprisingly uncrowded and peaceful
NTT DoCoMo Building
This gigantic tower resembling a granite Empire State Building, south of the station, is owned by NTT DoCoMo, Japan's largest cell-phone carrier. The upper part of the building is a mobile communications tower.
For people watching, the place to be is the large square in front of the station's Kabukicho entrance, next to the Studio Alta shopping center.
Tokyo Metropolitan Government Center
The two enormous buildings of this giant hive of bureaucracy are an Orwellian architectural masterpiece designed by noted architect Kenzo Tange. The main reasons to come here, though, are the twin observatories. At a height of 202 m on the 45th floor, they have some of the best views of Tokyo. The North Observatory is open daily from 9:30 AM to 11:00 PM closed second and fourth Mondays of each month, while the South Observatory is open daily from 9:30 AM to 5:30 PM until 11PM on the days the North Observatory is closed; closed on the first and third Tuesdays of each month. Last entry is 30 minutes before closing.
Hanazono Shrine
More remarkable for its location than its appearance, but it's a nice place to take a breather. There's often a flea market in the surrounding park on weekends.
Shinjuku-sanchome
and related red-light districts to the east of the station. It is perfectly harmless to walk around these during the day and marvel at the photo billboards of various male and female escorts on offer as well as the live gangster-types acting shady. While walking around this area should probably not be done with children, for adults the result is far more "cultural interest" than sleaze.