I will be visiting Tokyo come this October. I am very excited as this will make 3 international stops for my wife and I within 13 months. It has been amazing seeing a little bit of the world. Our first (2) trips were non-stop traveling with day trips/activities, train rides all over, etc.... Well that was fun and all, but it completely wore us out, so on this trip we have decided to just stay in one city and hopefully have a relaxing time. Our first (2) trips, I was very knowledgeable of history, location and customs/traditions of each country, having studied them since my college days, but I must admit, I do not know nearly enough about Japan..... I know I have plenty of time to get caught up and do some quality research, but I figure you folks could give me a start.....
So I want to know what is everyone's recommendations for Tokyo?
What do I have to see? Where and what should I eat? Is there an area you would recommend staying? Should I absolutely not go in October?

I might be up for one day trip, what should that one be?
So far all I have scheduled is arrive at the airport, then depart from the airport at the end, so I will need something to fill in between. I do enjoy visiting historical sites, architecture, and sporting events while on vacation. I will need my anime fix, so you can add that to the list.
Can't wait to see where everyone points me to!