Falcon Point's location ability states that "During the Movement Phase, you may spend $2 to move to any aquatic location and have an encounter there." Now, this would pretty clearly seem to mean that you have the encounter during the movement phase. Otherwise, mentioning having an encounter would be pointless. However, this...doesn't feel right. There doesn't seem to be any reason to have two encounters at a location just because you chartered a boat there. Is the ability just worded redundantly, and it means that you have an encounter during the Arkham Encounters Phase as normal?
If you do have an encounter during the Movement Phase, then the following exploit is possible: you move to Falcon Point, charter a boat to an aquatic location with a gate, have an encounter there (entering the gate's other world), cast Find Gate to immediately return to Arkham, and then close the gate during Arkham Encounters.