Just outside the Golden Gate Bridge in San Francisco Bay, we followed the footprints of a whale.

The footprints were real: flat slicks on the surface of the ocean formed when a whale’s flukes — the two lobes of its tail fin — push up water on a dive. Seabirds clustered above the same patch of water, interested in the fishy breakfast being stirred up there.

On this gray, drizzly morning, three adult humpbacks lazily circled our whale-watching vessel and dived down repeatedly to feed in the burbling waters where the bay meets the Pacific Ocean. We had barely begun our trip out to the Farallon Islands, 26 miles west of San Francisco, but we had plenty of company. Ten minutes later, out in the shipping lane five miles offshore, we came upon four more humpbacks. A gaggle of inert sea lions sat atop one bobbing green lane buoy, watching us go by.

San Francisco these days doesn’t feel so wild to me, but then I step off its shores and head out into the bay. I think about how stunning it must have been when explorers first arrived at its mouth. People commute mindlessly over the Golden Gate Bridge day after day without realizing that whales, sea lions, seals and harbor porpoises congregate here still. Venture a little farther out from shore, to the Farallon Islands, and you get a sense of what it was like to truly feel wild, remote, at sea.

Remoteness. Isn’t that what visiting a speck of land divorced from a larger speck of land is all about?

Named for the Spanish farallón, meaning a rocky pillar jutting from the sea, the Farallones were called “the devil’s teeth” by sailors in the 1850s for their ragged profile and treacherous shores, the cause of many a shipwreck. Today, the string of four groups of small islands totaling 211 acres is a National Wildlife Refuge, home to the largest colony of nesting seabirds in the contiguous United States. Five species of marine mammals all breed or haul out here, and great white sharks visit regularly to feed on many of them.

Though officially part of the city and county of San Francisco, the outcrops are uninhabited except for Southeast Farallon Island, where a handful of conservation scientists have a field research station. Permits to go ashore are rarely granted.

Although the Farallones are closed to the public, wildlife-viewing boats like the one run by San Francisco Whale Tours can approach them with care. Our captain that day was Joe Nazar, and our naturalist was Steve Wood, a cheerful biologist who conducts research on marine invertebrates at Dominican University of California.

A word of warning: This is not exactly a pleasure cruise. Going out to the Farallones can be a challenging expedition. “Come dressed for the moon,” the trip material told us. It’s good advice. I dressed for the moon in fleece and rain layers and I was still cold. The air temperature topped out at 55 degrees, but the wind, rain and sea spray from the vessel’s wake chilled to the bone.

Although the boat has a covered cabin with booth seating that recalls the interior of a cozy diner, it is not where you want to be when the boat is ricocheting off 8-foot swells on the open ocean. About halfway to the islands, one young woman came lurching out of the cabin, eyes wild. She headed for the railing and threw up off the starboard side of the boat.

(BEGIN OPTIONAL TRIM.)

About an hour and a half went by, during which the 20 or so other passengers and I stood outside in a hibernating trance, eyes fixed on the waves rushing

at us from the horizon. Then a Cassin’s auklet flitted by along the surface of the slate-gray sea, and I perked up. These protected seabirds nest on the Farallones. We were close.

As if to add to the drama on our approach to the fog-shrouded islands, the rain came in torrents, pocking the liquid-mercury surface of the sea. We arrived at Southeast Farallon Island in time to observe an inflatable Zodiac boat filled with cargo being lifted by crane from the water, with a few researchers looking on. Conditions on the rocky shore are too hazardous for a dock, so the Outer Limits, an aptly named fishing boat, had come on a volunteer mission to deliver provisions that had been handed off to the Zodiac. There is no fresh water on the island. Everything has to be brought in for these researchers.

Wood told us that sea lions, northern elephant seals, tufted puffins and other species had established zones on Southeast Farallon; as we cruised the shoreline, we got a closer look at a few of those neighborhoods. On one slope was an elephant seal rookery, with 500-pound juveniles lolling on the rocks. There weren’t any 2-ton adult males around that day (they can grow to the size of a pickup truck), but we could imagine. One juvenile can feed a great white shark for up to a month.

More than 400 species of birds have been recorded in the Farallones. We saw double-crested cormorants, red-necked phalaropes and common murres, which can dive hundreds of feet underwater to catch fish. That day the soundtrack to the islands was the cacophony of thousands of murres roosting together, which pretty much drowned out the songs of all other seabirds, save for the occasional gull squawk.

There are a lot of vagrants out in the Farallones. Wood explained that vagrants are, technically speaking, birds or other animals that don’t belong here, usually because they’ve gotten lost or blown off course: the odd sapsucker, for example, or the one northern gannet that took a wrong turn and has been returning to Southeast Farallon for four years. Gannets don’t live in the Pacific; they spend most of their time in the North Atlantic. We spotted the lone gannet’s yellow head bobbing as he perched high on a dark granite outcrop, exhibiting nesting behaviors. His plump, white-feathered body stood out against the smaller birds. According to scientists, he is the first known northern gannet in the Pacific.

The strangest vagrant species of all, though, was Homo sapiens: A man wearing a fluorescent pink swim cap — no wet suit, despite the 53-degree water — suddenly emerged from a small boat drifting near us and swam off to a buoy on the southeast side of the island. He seemed unconcerned about sharks. As we watched the swimmer front-crawl his way toward shore, Nazar shook his head.

“When I was a kid, people used to come and shoot sea lions off that rock from the back of their boats,” he said. Now the sea lions are back in force, he added, and we humans look for other ways to get a rush.

Later, on our way back through the Golden Gate, we had the most intimate encounter yet with the humpbacks, who seemed to be performing for us as they rolled and flipped their flukes. Suddenly an awful smell washed over the boat. Our marine biologist laughed when he told us that it was nothing more than the stinky baleen breath of a whale.

— If You Go: Farallon Islands whale-watching and natural history tours are offered by San Francisco Whale Tours (sanfranciscowhaletours.com; $99 for six hours) on weekends only, year-round.