I was in Tokyo in March for a couple of does. I had a fantastic time. We stayed in the Shinjuku area, easy walk to Shinjuku Train Station which was where we met up with the Subway, take the Subway everywhere.
I recommend Shibuya at night, kinda times square-ish, lots of young people, lights, things to see. Walking around Harajuku on a weekend afternoon is also something that was cool to see, so many people walking around and shopping, the Meiji Shrine was there, and that was probably my favorite shrine. I also did Tokyo tower at sunset, that was really touristy but I enjoyed it. Ginza is a big shopping district in Tokyo, we walked around some of the department stores, which are really unique. I recommend picking some food and eating at a department store, in the lower levels of most of them they have a food court type thing where you can pick some food out and eat it. Finding a place to eat it is kind of tough though. We went upstairs to a restaurant in the department store and ate some tempura and udon noodles. I wasn't a big fan of the Roppongi area, it seemed to me like it was a really international area, like the area where you find a hard rock cafe and stuff, a good place to go if you start needing some American food. Food wise, my three favorite meals were:
1) Shabu-Shabu - you get raw meat and have a pot of broth to boil it with vegetables and some sauces. This was my favorite, I loved it. We were definitely confused as to how to do it at first, but just be creative and watch how people around you do it.
2) Went to a restaurant in the Asakusa area and had a "beef-cheek hot pot" it was delicious, and came in a pot with literally fire keeping it warm underneath. It was also delicious.
3) The Udon noodles and tempura at the department store.
Eating can be tough as many restaurants' names are in Japanese, and many don't have English menus. This was definitely the most challenging part for us.
HollywoodBQ gave me lots of good info too, more-so than I have provided, I'm sure he'll see this thread and respond.