I wasn't sure how to interpret your ask, so I just put recommendations for lots of different possibilities.
If you're looking for a movie or drama set in Asia with a predominantly Asian cast and an American lead:
- The Forbidden Kingdom
- The Karate Kid Part II
- The Last Samurai (I haven't seen this one yet, so I'm not sure if there is romance)
Dramas where the leads are from different countries / kingdoms but the actors are from the same country:
- Empress Ki
- The Princess Wei Young
- General and I
Drama where the leads are from the same country but one of them grows up abroad:
- Kill Me Heal Me
- She Was Pretty
- I Need Romance 3
- To the Beautiful You
- City Hunter
- The Heirs
- Attention, Love!
- The Masked Lover
- Oh My Venus (to a limited extent, but the third male lead also fits)
Dramas where one of the lead characters is "foreign" in the sense that they aren't human and come from some kind of other world:
- You Who Came from the Stars
- Hi! School - Love On
- Hwayugi
- Bride of the Water God
- W Two Worlds