A taxi from Narita airport into the heart of Tokyo will cost your over $200 USD!  Try the airport bus for $10 or $20 to a major hotel and then using a cab or subway for the remainder of the journey.

Safe city no need to worry

Tokyo's transportation system is one of the most extensive and complex anywhere in the world. It's hard to find a place in central Tokyo that can't be accessed by train, and more than likely any hotel that you could choose to stay in has a train station within a short walk from it.

Firstly, getting into central Tokyo from the Narita International Airport can be a hassle if you haven't thought about it. There are two fast routes into central Tokyo from the airport. The Narita Express operated by JR runs into central Tokyo approximately every 30 minutes with services running to Tokyo, Shinagawa, Yokohama, Shinjuku and Ikebukuro stations. There's also the Keisei Skyliner which runs express to Ueno in northeastern central Tokyo.

It helps if you purchase a JR Rail Pass from your home country before you travel to Japan (this allows you to travel on all JR services using this pass as often as you like including the Shinkansen, but not Nozomi services).

Within central Tokyo itself there are many rail lines criss-crossing the area. The most useful of these are the Yamanote Line (which loops around central Tokyo), the Chuo Rapid Line, Chuo-Sobu Line and the Keihin Tohoku Line. These JR services run every few minutes and serve much of central Tokyo. It's preferable to use JR services as they are the most convenient to use, but certain places such as Roppongi and Asakusa can only be easily accessed by the subway.

Maps for the JR East system can be accessed here: http://www.jreast.co.jp/e/info/map_a4ol.pdf

Maps of the Tokyo subway system can be accessed here:
http://www.tokyometro.jp/rosen/rosenzu/pdf/rosen_eng.pdf

If you have JR pass you can use it inside Tokyo. You can go to the mot of the main attraction.