We just came back from Japan for a 9 day visit and we spent about 5 days in Tokyo.
We like Tsukijishijo築地市場, need to get up early and take the first subway at 5 to get there if you want to watch auction. You can eat sushi breakfast around there.
We also like Edo-tokyo museum, free English docent tour, weekend has short performance. A few hours.
Imperial Palace皇居 and 靖国神社 take half a day.
Asakusa浅草 is very nice. Ueno上野 has a lot of museums that we don't have time to visit, just walking around does not take a lot of time.
Shinjuku新宿: got to visit Tokyo government building 45th floor, ask for free English guide on the top floor or at the bottom floor for a tour of the building.
We also like Meiji-jingu明治神宮 and watch shibuya渋谷crossing.