N.Y. Komachi(1986)

Konohana Shino lives in the Meiji era of Japan. As her father's only child, she was raised like a man. Now a young woman, Shino has top grades in school and is the top fighter in the dojo. But one day, her little brother is born, and her father decides that it's time for her to be a woman. He insists she quit school and the dojo, dress in the confining clothes of a woman, and marry a guy she has no interest in.

Shino has no idea how to deal with this unexpected and unwelcome twist in her life, until she happens across the foreigner Daniel Irving. After she saves him from thugs, he tells her about all the opportunities for women in New York. Determined to find a better life, Shino runs away from home and stows away aboard a foreign ship. Two things don't go according to plan-- Daniel is aboard the ship as well, and it's going to Hokkaido, not the US. Even so, this can still be the beginning of a new life for Shino, one that includes a lot of Daniel. But even if she finds that she loves Daniel, this era is not an easy one for marrying foreigners...

(Source: MangaHelpers)