If you are in the Shinjuku area and need to get an overview (literally) of Tokyo, this is the place to be. The Tokyo Metropolitan Government complex is a series of buildings with striking architecture that have an observation deck on the top floor for public viewing, FREE public viewing I might add! Anything, within reason, that is free in Tokyo, jump at the chance!
Ride the public elevators with 20 of your newest, closest friends (please realize personal space in Japan isn't what it is in most other places) to the top of the Tokyo skyline. You will be afforded far-reaching views across all of Tokyo, and if lucky (and it's very clear), Mt. Fuji will be in the distance. Spend some time getting your bearings straight in this massive city. Break out your guidebook and try and decipher where the sites you want to see are. I spent about an hour here and really took in the surroundings. It gave me a better understanding of the distinct districts that make up Tokyo proper.
While up top, I also spied a small park that was having a "flea market." Always on the lookout for a good buy, I made my way down and made a few inexpensive purchases. Keep on the lookout for unique adventures. They are always out there to be had.