College academic transcripts seem to be the best proof of living in the US after getting your license.
If you have to retake the exam (as most of us do) be prepared to shell out about 3500 - 4000 yen per retake.
Many driving schools will offer a special course that will only teach you how to take the driving test. In Saiki, the class was an hour a day on four separate days for 9000 yen. That's cheaper than going to the Oita test course on Saturday and renting a car and instructor for an hour. My recommendation would be to go to a driving school if possible so you can learn how to pass the test. That, and take the test before your international license expires. In July and August is when all the JETs go to get their license and getting an appointment can be tricky.
When you go to take time off to take the test, ask your supervisor if there's a special leave (tokkyu 特休) you can take instead of nenkyu. At my school we can get special leave for official business that we have to take care of during the week (such as sorting out paperwork at city hall or taking your driving test). If possible, ask if you can take that. They may or may not let you, but it’s a worth a try either way!