I just got back from Japan on Sunday. While Tokyo is sick, it really feels like New York City, where I was born and have lived all my life. Some parts of Tokyo feel like a more crowded, but bigger manga-covered Times Square. On the other hand there are much quieter parts of Tokyo and more upscale areas. I stayed in Tokyo for about 3 days and I really feel that that is more than enough to experience the neon-covered parts of the city.
A little note on transportation: Taxis are not worth it. The public system is much more efficient (the average delay for trains in Japan was 36 seconds, in 2007) and much cheaper (¥180-260 one way for the Tokyo Metro). I live in a fairly wealthy family and we (my dad and I were the only ones who went - father-son trip) pretty much took the subway around the city. This was not a claim. A side note is that it never got as cowded as the videos on Youtube show, but sometimes this really does happen, especially during the morning/evening rush hours.