A bit south of Narita Airport is a small circuit called Narita Airport. The length is only 800 meter but due the large amount of corners and relatively low average speed fast lap times are still between 40-50 seconds. The straight is only 110 meter and the width of the track is quite narrow with 8 meter.
It depends on the day, but free driving is often possible. Make sure to check the calendar on the website. Free driving starts at 9:00 and ends at 12:00 for the morning session and the afternoon session is from 13:00 until 16:00. The price is 2500 Yen on weekdays, 3000 Yen on Saturdays and 3500 Yen on holidays and Sunday’s for 1 hour of driving. It is also possible to do a 3 hour package on weekdays for 5000 Yen.
The website has a detailed overview with fastest lap times per tire type, engine power, etc. Regularly special events are organised for grip driving or gymkhana. Drifting is not allowed unless a special event takes place.
Narita Motorland is approximately 1 hour driving from Tokyo. There are no public transport connections close to the circuit unfortunately.
A link to the website can be found below:
http://www.narita-motorland.com/
And a link to the location on Google Maps: