Shinjuku is an office/pleasure district, located in the southwest of Tokyo around Shinjuku Station. It is one of the busiest districts in Tokyo along with Shibuya and Ikebukuro. The area is always crowded, be it day or night. On average 3.35 million passengers per day used Shinjuku Station in 2013; the station currently holds the Guinness World Record.
Shopping or eating out, there is always plenty to do in Shinjuku
To the east of Shinjuku Station, there are Isetan, Mile, and Lumine department stores as well as Kinokuniya bookstore and a variety of famous restaurants. Studio Alta and the police booth near the east exit are often used as a meeting point. Since it is always very crowded, it might not be a good idea to meet up here.
In Western Shinjuku, there is Keio Department Store as well as many other department and electronic appliances stores, such as Yamada Denki. If you go further, there is a skyscraper district that hosts various office buildings and hotels.
To the south of Shinjuku Station, there are also some high-rise buildings as well as Takashimaya Department Store and Lumine the Yoshimoto, a comedy theater. A lot of people use this place as a meeting point as well. In the evening, one sometimes can see amateur musicians performing.
In the North, there is Kabuki-cho, a pleasure quarter that has many hotels and restaurants. It is sometime called "The Golden Quarter" and it has over 200 eateries and drinking establishments, lined up along the street. It might be scary at first but it is also a part of Japanese culture.
The nearest station is JR Shinjuku Station. There are a lot of parking lots, so it is also possible to visit by car. However, please allow some extra time given that the area is extremely crowded.