I've been to Japan six times now; most recently returned last week.
Everyone is right that
ABD can't definitively do Tokyo in a few days, I don't think anyone can.
Top things people usually ask about/I see repeatedly on tours:
Shibuya Crossing (and pet Hachiko)
Tokyo Skytree and/or Tower (you could also visit the Tokyo Metropolitan Building instead for a free view, if a view is all you want)
Visit a temple (senso-ji usually, but if you happen to visit during a festival, whichever one is celebrating jumps to the top)
Visit a shrine (Meiji-jo usually)
Visit their parks; Ueno, or Shibuya usually, but there are so so many..
Visit the Imperial Palace (ok this is also mostly a park too... unless you happen to be there over new years or the emperor's birthday)
Cultural events - tea ceremony, kimono dressing/pictures, staying in a ryokan to experience kaiseki and onsen, etc.
Visiting Tsukiji (less often now that the auction isn't what it was) but certainly getting the freshest sushi at the markets for breakfast
Shopping in Akihabara if you're into electronics or anime (play in the arcades!), Ikebukuro as well for anime, or Kappabashi for kitchen stuff in Asakusa. Stop by Ginza to shop or at least have the eyeballs pop out of their sockets at the prices. Find an outdoor street like Nakano Broadway to peruse.
Visit museums - like most cities they have nice art museums and national museums to peruse.
See a sumo or baseball match
See Kabuki or Noh performance
EAT. You can eat the most expensive food of your life or just pop into a convenience store - its all good! They are masters at seasonal foods and many towns and areas have claim on things like 'best strawberry' or melon or what have you and its soooo gooood when they are in season! They have some very very old places which are fun IMO too... I just learned about Rairaiken, which has been dishing up ramen since the 1910s. We had a cat robot serve our sushi to us last week. Its just all so much to take in, lol.
Then of course there are the things further out like Fuji, Hakone, the Ghibli museum or Disney....
edit - totally forgot about Shinjuku because nightlife and red light districts are not my bag, but they are some folks'.... it also has some iconic department stores, hotels, and restaurants well worth visiting or staying at. The bar from Lost in Translation is atop the Park Hayatt.