I went to Tokyo about five years ago and loved every minute of it.
Before you go acquaint yourself with Tokyo's massive
rail system. It can be quite
confusing at the onset. Don't wait until you get there before you study the lines and the different ticketing options.
Here's a few places I recall in no particular order
Ueno Park
Sensoji Temple
Tsukiji Fish Market - a must see - go very early in the morning
Tokyo Tower - to fully appreciate how massive Tokyo is
Mount Fuji - we took a Gray Line all day English speaking tour. Transported there by bus. Had a great time with Brits, Aussies, Canadians and a few more Americans. On the way back we toured the
Hakone hot springs area. Then we returned to Tokyo via the
Shinkansen. Was a great day, highly recommended.
Imperial Palace - not much access but very placid as you would expect, this area is surrounded by other government buildings and embassies.
Ginza district - high end shopping and entertainment - make sure you visit the Sony flagship store
Shinjuku in the evening for dining. Generally found that the evening hours all the areas around train stations were overflowing with people hitting bars and restaurants. There are literally hundreds of restaurants within Shinjuku serving every type of cuisine imaginable. We were eating at a Chinese restaurant when a 6.2 earthquake struck about 20 miles out in Tokyo Bay. That will get your attention!
Akihabara - hundreds of electronics and technology shops
Roppongi - kind of a funky area, very diverse and fun, lots of restaurants and entertainment choices.
I really want to go back. I was extremely impressed with the culture and how civilized it was.