Atami is not a bad little town. Its got a beach, great fireworks displays in the Summer, and is less than an hour from Tokyo by bullet train. I live across a mountain range, but only about 20 km away from there.
No need to worry about your Japanese language skills, you'll get by without too much trouble, and people are quite friendly to struggling, fresh-off-the-boat foreign English teachers. You and your girlfriend will have a great time exploring the somewhat quirky culture of a Japanese resort town. Atami even has a "sex museum" with a giant coin-operated phallus ride... or it used to.
You should be able to join a local basketball team, but be prepared for some biased officiating if you are tall and reasonably good.