Tsukiji, early in the morning, then back in that area at night for really fresh sushi
Harajuku, just to see it
Shinjuku at night
Kabuki-cho at night can be sketchy. Get an insider
Tokyu hands was actually pretty cool
Yokohama was ok
Asakusa was a cool area, way cool temple. Kamiya bar nearby is one of the oldest, great experience.
Get a suica card, best way to get around on the subway
Ginza to walk around and see high end shopping.
Tons of great parks to hangout in, can't remember the names, one was in shinjuku close to our apartment
Sushi is a must
Tonkatsu is a must. I prefer Tonki, near the ebisu station on the yamanote (green) line
Ramen is a must. Any ramen stand close to a train station is typically good. If you can find kohmen, I like that. There are places in harajuku and roppongi that I have been to, get the spicy stuff.
For authentic ramen, I like ramen jiro, a few blocks north of shijuku station.
There are a ton of lunch counter type places that you pay first then sit down. They have a machine, usually with pictures by the door. Pay, get your ticket then sit down.
Make sure you have cash, fewer places take cards.
If you can find okonomiyaki get it, normally it is an Osaka dish.
Also if you can get a unagi bowl get one, especially around may when it is in season.
Also go to shibuya one night, very cool lights. And say hi to hachicko.