You can't miss Akihabara, of course.
Nakano Broadway is also a interesting place if you like manga and anime (although they are focused on more retro stuffs)
If you like animations from JUMP manga magazine, such as ONE PIECE, NARUTO, Dragon Ball, Breach, etc., Jump Shop maybe your destination. They sell many products using characters from Jump manga magazine.
Ghibli Museum is a must-go, too.
Also there are many places in Japan used in anime, so visiting these places "Seichi (聖地) - sacred places" is kind of hot things to do within anime lovers :)