Shinjuku is one of Tokyo‘s 23 wards and is a huge entertainment, shopping, business and (some) government district. Basically Shinjuku is a city within itself but is really just a (big) fraction of Tokyo. Shinjuku is very famous and has been in many movies including most recently “Lost in Translation” and “Kill Bill.” Shinjuku always seems busy no matter what time of day you go there and Shinjuku Station, is one of, if not the busiest station in the world. Shinjuku has a lot of really cool and large buildings (Tokyo Metropolitan Government Office, for one which offers great views of Tokyo) as well as a lot of people, shops and restaurants.
If you go late at night it is not uncommon to see drunk, passed out salary men sleeping on the streets or friends carrying another friend who is too drunk to walk. I recommend going, but do be careful if you wander into Kabukicho, the entertainment, drinking, adult and red light district, which has a lot of ties with the Yakuza (Japanese Mafia). In general, this area is fairly safe compared to the rest of the world, but compared to the rest of Japan it is a little unsafe. That being said, just don’t go picking fights with anyone and you should be fine.
For more information please see the Japan-Guide.com.