Teutonic Order had it's base first in Starkenberg castle near Tripoli or Acre, until it fell to Baybars.
Then they had their HQ in Venice until 1309 I think, when it was transferred to Marienburg in Prussia (or modern day Poland)
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Knights Templar had their base in Jerusalem and after it fell, I believe Acre, but not so sure.

Hospitallers relocated to Rhodes, and later to Malta. Dunno if Beaufort or Krak des Chevaliers were their HQ before they fell.

Spanish Orders were in Castile.