I heard a rumor that Godzilla was attacking Shinjuku!
Shinjuku station is the busiest station in Japan. Lots of lines converge at this station so it's a very busy hub for commuters and tourists alike.
Many tourists visit Shinjuku when they come to Tokyo. However, I feel that there are not that many things to see in Shinjuku. The Godzilla statue in Kabuki cho is one of the few really amazing sights.
If you want a closeup of Godzilla's head, please go into the Gracery Hotel. On the 8th floor is a small viewing area which is open to the public, even if you are not staying at the hotel. From close quarters, the statue is even more impressive than from below.
Next up, take a look at the Golden Gai street. These narrow alleys, bordered by small bars, were home to an underground market after WWII, when food and goods were scarce. Gradually Golden Gai became known as the red-light district of Tokyo. When prostitution became illegal, the area changed its focus once again.
These days the area provides alcohol to night revelers in a variety of bars. My recommendation is, don't go into the bars! Some of them charge relatively high cover charges and will rip you off when it comes to paying. It is much more interesting to wander through the streets and feel the atmosphere. Save your money for later.
Next to Golden Gai, there is a shrine called Hanazono Shrine. The god of this shrine is said to protect actors and performers, so it is sometimes visited by celebrities. This is a good place to take some pictures and escape the crowds.
So what does Shinjuku have to offer? Honestly, there are not that many things to see. The robot restaurant seems to be popular among tourists, but it has become fairly expensive, so I don't recommend it. There are lots and lots of shopping opportunities in Shinjuku, so if you want to shop, Shinjuku might be a good place to visit.
The main attraction of Shinjuku is the fact that so many people pass through the station and area. It can be quite thrilling to see the throngs of people crossing the street and moving through the station.
Another place, which is free and offers great views of Shinjuku, is the Tokyo Metropolitan Government office. There is a free observation deck on the 31st floor and you can see great views of the city from 202 meters up, although the view is not a 360 degree one. The observation decks are open from 9:30 in the morning til 11:00 at night.