By all means apply, but ask some hard questions before you accept.
I did 2 years there in the Navy, 95-97, and it's a neat place but WAY expensive and a huge culture shock.
Rent was $1600 for 800 sq. ft., 2 bedrooms. Paid in cash every month. Pay other bills at the 7-11 (no kidding) in cash too. Some things may have changed since then, but when we were there, it was a predominantly cash society. No checks. Bigger stores took some major credit cards. No way to pay bills on line.
Grocery prices are out of sight. $5 for an apple, $20 for a watermelon were some of the things I remember. Those were on the high end but you get the idea. Expect to pay at least 50-100% more every month for food. Can you take the cold? Electricity could easily run $400-$500 a month in the winter if you're not careful. Most folks supplement heat with kerosene heaters and shut it off at night, restart in the morning. Lowest temp I saw in the AM was 35 degrees. Talk about shrinkage. This was in the Yokohama area. I hear the northern houses were better insulated, but not sure.
People are very friendly in public, but stand-offish in the neighborhood. Didn't meet many folks there, but Japanese people will ALWAYS help you when you need it.
Would I go again? sure. Is it high on my list? Not particularly. It's a cool place, but after a few years, you'll want to return to the land of the big WalMart.
If they pay enough, consider the job, but see if you can find someone who's been there more recently for data. Oh, and go to your video store and rent "Mr. Baseball" starring Tom Sellick. Most of the culture / lifestyle stuff is pretty close. To me it was funnier after living there.
Good luck!
Catfish