I like seeing k-dramas set in other countries (even if it's only the beginning of the drama) I think it feels more special seeing main leads falling in love with each other in another foreign country :D

here are some I'm thinking of: The Package, Devilish Joy (first half of ep 1), Encounter (ep 1), Legend of the Blue Sea (beginning eps), Man Who Sets the Table (beginning eps), Goblin, Black Knight: the Man Who Guards Me, Are You Human Too, Memories of the Alhambra, The Third Charm (?), Terius Behind Me (only a few scenes though)

Spring Waltz

Time Between Dog and Wolf 

Beyond the Clouds (They don't come face to face there, though, iirc)

Full House

There is also Love Rain, Naeil's Cantabile (at the end instead of the beginning), Hooray for Love, and of course Heirs.  Didn't like these as much for different reasons.

A show that is airing right now, 

Memories of the Alhambra

  • Descendants of the Sun - Made up country "Uruk"; they filmed in Greece
  • Mr. Sunshine - Japan (the ML also spends time in the US)
  • The Hymn of Death - Japan
  • Goodbye Mr. Black - Thailand
  • Jealousy Incarnate - Thailand
  • Misty - Thailand
  • The K2 - Spain (a brief encounter)
  • Empress Ki - China
  • About Time - China
  • On The Way To The Airport - Malaysia (I can't remember if the ML and FL were ever both there at the same time, but there were location shots and they bonded over their shared connection)
  • City Hunter - Thailand (the FL doesn't spend anytime there, but the ML grows up there and first sees her picture while he's there)