I would also highly recommend teaching in Japan. I taught in Japan for 16 years, had my own English school and started a corporate ESL consulting business as well.
I, myself, would stay away from the JET program or any other program or school that would hire you abroad for three reasons.
A) Money: The programs that offer jobs to teachers overseas generally underpay their teachers. They often charge outrageously for housing or other "services" as well. You will do much better, especially if you have experience teaching, by forging your own path.
B) Quality of Life: Schools and programs that hire you overseas are, generally (not always), looking to fill vacancies in their systems far from the beaten path. Teaching in a larger city, Tokyo, Osaka, Nagoya, Yokohama etc. etc. gives you many opportunities to supplement your salary and interact with other professionals. Until you have fairly good Japanese language ability, living in the far off Yamagata-ken or Aomori could leave you feeling very alone and isolated.
C) Your development as a teacher. If you decide that you would like to become a university professor or write texts or, essentially, engage in any kind of professional development or bounce ideas off of fellow native speaking English teachers, you want to be in a bigger city.
I would also say that very few people I have met have truly enjoyed or benefited from the JET program. You are essentially, in most cases, treated as a "student teacher" by the Japanese classroom English teacher. There are often some weird twistys happening because of the fact that they are in control of the classroom and yet their English is limited to terrible and they and the students know it. That is why experienced English teachers are often not offered JET positions. The ministry, Mombusho, knows that real teachers are going to have issues with what is going on in the classroom.
I went to Tokyo on the advice of a friend, who shared basically what I have shared above. I am retired at age 53, very comfortably, because of the wonderful people of Japan and the amazing experiences I had. I too am willing to share with anyone interested.