Shinjuku
Shinjuku is considered the more "adult" hang out spot, opposite of Shibuya. There are many places to eat and drink in Shinjuku and also a theater with Godzilla popping out from the roof. Shinjuku Gyoen National Park is a must see if you want to just take a stroll and admire wildlife in a busy city.
There is a really nice view you can check out for free at the Tokyo Metropolitan Government Building. You can go there during the day to catch a glimpse of Mt. Fuji or at night to see all the neon lights from the busy nightlife city.
