...caligraphy works much better with American chicks.
"Here, let me show you what your name would look like in Japanese..."
Whip out your fude-pen, the more elaborate the better, and write her name down on a piece of washi to take home. I've never met an American who was not impressed by that sort of stuff.
If you are seducing a J-girl, I would suggest doing something in the opposite direction.
I don't know where you live, but in some parts of America, it is nearly a hundred-fold cheaper to go horseback riding or sailplane flying than in the more expensive parts of Japan. Depending on where she is coming from, these things could become a once-in-a-lifetime experience. And there is the old standby - firearms. You can't own guns in Japan, so shooting a gun is definately a rare experience for a J-girl.
There is an old psychology study that says that a girl is more likely to fall in love with a guy she meets in the middle of a suspension bridge. And there's also the old "Waterloo Bridge Syndrome". Since you stress hormones and love hormones have almost identical effect, getting her excited when she meets you is sure to work in your favor.
Jeff Bridges uses horses as "foreplay" in the movie "Jagged Edge". You can use a visit to the shooting gallery in the same way. And the screaming excitement that girls have when they meet a good looking blond gaijin in the streets is an element of the "suspension bridge" effect you get in Japan.
Use your imagination, but I don't suggest caligraphy.