“Japan's pop/anime-culture hub!”
I would recommend anyone visiting Tokyo to visit Akihabara, primarily because it is just so weird and unique. Wether or not you are an anime/manga fan, Akihabara is well worth seeing for its unique array of stores. Here you can shop (or window shop) for electronics, figurines, anime and manga goods, dolls, model trains, and just about any other toy you can think of.
Another fun activity is trying out the number of arcades in the vicinity (the Sega arcade is particularly notable). The prices are fairly reasonable, and you can play some games that I have seen no where else - one such was a game where you were a salary-man who had to flip over a table (presumably due to stress?) at just the right moment in order to get higher points. Also don't forget to try Purikura (selfie machines), which is a funny thing my wife and I do every time we visit the area.
Best visited around twilight while the shops are still open and the iconic neon signs begin to light up!