Seeing the area next to Tokyo Narita during layover
I have never been to Japan but will be stopping over at Tokyo's Narita airport for 3 hours and 45 minutes on the way back from Bangkok. The layover is during the afternoon so I though I might rush a couple of hours of touring before I have to check in for the next flight.
I understand there is a city called Narita Japan a few miles from the airport where I could go and see a typical Japanese town for an hour or so.
I looked at the Narita web page and it said that they discourged people leaving the international terminal area if they had a connecting international flight but it could be done with a visitors pass.
Has anyone done this? If so:
What train did they take to the city of Narita? Are there signs in English? Was it a hassle getting through passport control as a transit passenger? Did you have to pay a departure fee because you left the secure arrivals area? What train should I take? What will happen if I miss my connection to the USA, huge fine? Am I crazy or should I be a good boy and sit at the gate for 4 hours waiting for the next plane to Chicago like everyone else? Thanks.