Final answer:
The story "The Silver Outrigger" takes place near Mosquito Inlet and New Smyrna on the eastern coast of Florida, depicting a nautical adventure.
Step-by-step explanation:
The excerpts provided indicate that "The Silver Outrigger" takes place in the vicinity of Mosquito Inlet, with references to St. Augustine, Dare's Gift, and a possible life-saving station. The setting seems to encompass both the coastline and sea, reflecting a nautical adventure with themes of survival and camaraderie amongst the crew of a boat. Particularly, the mention of New Smyrna and the lighthouse at Mosquito Inlet helps to anchor the story in a specific geographical location along the eastern coast of Florida.