Tokyo actually consists of different cities that have their own special attractions. Since it doesn't make too much sense to tell about all of these different cities as if they were one city, we have subdivided Tokyo in the following way.

Akihabara has he largest concentration of electronics shops in the world.
Asakusa is famous for its temples.Ginza has fabulous shopping opportunities for equally fabulous prices. It is an extremely busy place.
Marunouchi is the area around the huge Imperial Palace.
Roppongi is the place to go to for nighlife.
Shibuya is north of the center and has shrines and trendy shops. Shinjuku offers good shopping facilities and high skyscrapers.
Ueno has a beautiful park, some good museums and temples.

To get from one end to the other, the best thing to do is to use the metro system. Although it takes some time to get used to it, it is by far the fastest and cheapest way to get around. For more info see tokyo,getting around:the getting around section.

Among the highlights of Tokyo no one can afford to miss are: the Sony building in Akihabara, the Imperial Palace, the temples of Asakusa, Korakuen Graden, the sight of the sacred mountain of Fuji in early morning (rare most of the time it is too dusty), the Tuna auction at dawn in Tsukiji Market. If you can, try to see a Kabuki performance as well.

Tokyo is not a cheap city to visit. The general price level of Japan is among the highest in the world and prices in the capital are even higher then elsewhere in the country.