It depends on your interests.
Shinjuku Gyoen Park is beautiful to take a walk if it is a sunny day. If you like bar hopping, head to Golden Gai, Omoide Yokocho, or Shinjuku Sanchome District. There are tremendous amount of bars there.
If you would like to get the great city views, visit New York Bar in Park Hyatt. The bar is used for the location shooting in the film Lost In Translation.