Kabukicho, Golden Gai and Shinjuku-Nichome are in East Shinjuku.
The area around the east exit of JR Shinjuku station features shopping, dining and izakaya.
It isn't a red light district (it's somewhat safer than Kabukicho itself).
Kabukicho is a large entertainment district to the northeast of Shinjuku station.
The area has many izakaya and restaurants. It's also a red light district that's considered amongst Tokyo's most dangerous neighborhoods.
Information not available in English