Megapolis Tokyo has many downtowns. Ginza; high end shopping district, Shibuya; shopping and night life district for young Japanese, Asakusa; the oldtown of Tokyo, Ikebukuro; Anime fan district and of course, Shinjuku.
Shinjuku is definitely the king of downtown in Tokyo. Shinjuku includes the busiest red light and night life area in Far East; Kabukicho. Then, the significant difference among those downtowns is that Shinjuku is also a business district. Tokyo metropolitan government's office is located at the west side of Shinjuku. The capital of Japan is Tokyo but capital of Tokyo is Shinjuku.
Therefore Shinjuku is busy during weekdays and weekends, from morning to evening. Shinjuku station is not the main station of Tokyo but the busiest station not only in Japan but also in the world. On the other hand, Shinjuku station does not handle any Shinkansen.
If you have a day off in Tokyo, Shinjuku is the place where you should visit. Enjoy the awesome skyline view from the observatory of metropolitan government office, take a walk at Shinjuku gyoen national garden, buying electronics at megastore and dine at the restaurant.