The area with the most skyscrapers in Tokyo, Shinjuku is often consider the main downtown, Shibuya being the second one, but it really a matter of opinion since they’re probably both equal in popularity. Whats differentiate them the most would probably be they target audience, Shibuya obviously is aiming more to teenager with 109, HMV, etc.. and Shinjuku on the other side had more of an adult crowd, with all the izakaya, bars, host and hosted club and the infamous Kabukicho.
Shinjuku Station is not only the busiest station in Tokyo, but in the whole world. With 3.5 millions passengers going trough it twelve lines everyday it one of the worst place to get lost in Japan.
Since there is so many people outside Shinjuku Station, you can often see and hear protestant and political group literally screaming their message trough megaphone. Personally I don’t know why this is legal, it really annoying.
This is the famous gate that mark the entrance to Kabukicho area. The most famous "redlight" district in Tokyo. But compare to similar places in big american cities, it is very safe, after all Japan is known to have one of the lowest criminal rates in the world.