The zither is my favorite... from any area of the world. I actually play the Chinese Zither.
When I go to the Renaissance festivals, I love to hear the medieval music have a zither with it. Adds a lot.
Other than that, I'd say the Celtic harp is divine stuff.
Knight Templar n. pl. Knights Templars or Knights Templar 1.A member of an order of knights founded about 1118 to protect pilgrims in the Holy Land during the Second Crusade.
Asia's had some pretty cool instruments. I think there was one which was kind of like a guitar.
I would go for the ukulele or the banjo, but sadly they aren't medieval.