I don't know if anybody wants to play with military knights, but if we did Montfort Castle (wiki entry)
was an admin site for the Teutonic Knights who wanted to move out of Acre, and in 1228 they get large donations from the Church to finance fortifying it - the new castle becomes the headquarters of the Teutonic Knights in the Holy Land in 1229. I was checking out different castles in the area when I came across this fact, and as we're starting after the Grand Tribunal of 1228 there's the possibility of us taking an alternate history view where magi with deep pockets or political conections within the church try to influence the Teutonic Knights.
The idea of a hospital is also good - allows the chance to use all those pilgrimage/hospitality related virtues from Covenants to make an interesting covenant.
Near Antioch you could arguably be both in a War Zone and on a Tribunal border as the area is both contested between little Armenia and Tripoli as well as being arguable for either the Theban or Levant tribunal. Which definitely fits the role of "interesting".
Are you still interested in pursuing Aqaba as well?
Another interesting place could be the Sidon Sea Castle. It's in Muslim territory from 1187, and it will be reconquered by the crusaders 100 years later.