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.

take the subway. cabbies don't know the whole city and rarely more that just the few touristy areas.

Safe city no need to worry

Be sure not to confuse trains. Many Japanese know English and are usually very kind to foreigners when in need of finding out what train to get on next. It is always a good idea if you are interested in learning Japanese to learn phrases such as "Where is the train station?" or "What time does the train depart?".

A surprising city, but nothing to comapre with the rest of Japan

ALWAYS get to the train systems before 6 am. That's when rush hour is and it will be very awkward. ALWAYS remember that they don't take cash from the hand but in a small dish they give to you. Try to stick to cash only, there are virtually no stores or restaurants that take credit cards.
Try to stay in a Ryoko-Inn. You'll get an authentic feel to Japan's ways better. PACK LIGHT CLOTHING! It's 90% humidity most of the time and you want something that can breath..

Walk with the "flow of traffic" or people will look at you weird! Their right is your left!

I found the transportation incredibly easy. Everything was color coded and phonetically written on the maps and in the stations. Just make sure you have a good map and pay attention and you should be just fine. This was also one of my first experiences with public transportation so for me to be able to navigate easily is saying something.

Don't lose your rail pass!

Pricey!  Get a book and use the subway. Very easy to use, it's all in English.  Expect to pay 3 to 4 dollars (US) per person, per one way subway trip.  Lots to see.  Make sure you check around for Hotels.  The Villa Fontain was inexpensive but very nice.  I'd go back.