It's actually not the FAA that has say over places like Cannon Beach - it's NOAA and the US Fish and Wildlife Service. All of the small islands and sea stacks along the Oregon coast (1853 of them) are considered
protected wildlife refuges and the rules are explicit that you cannot fly under 2000' directly above them. The Oregon Islands National Wildlife Refuge rules apply to each island or seastack and NOT the water in between them so you can legally fly around the islands but not over them. This is actually quite lenient compared to the Washington coastline from Neah Bay down to roughly Ocean Shores where ALL flight activity has to respect the 2000' flight floor. That one covers all beaches up to the high tide line.
The 2000' flight floor is not restricted to manned aircraft and does apply to drones. The laws specifying FAA jurisdiction over the National Air Space has an explicit exemption for this type of refuge.