Your flight to Iceland will unquestionably land in Reykjavik. Before heading out of the nation’s capital to explore Iceland’s famed and fantastical glaciers, volcanoes, and surreal landscapes, spend a little time here to see some things you won’t find anywhere else in the country. These are my favorites.

#1 Soak in the Blue Lagoon

If immersing yourself in an enormous pool of milky blue waters that are rich in blue-green algae, mineral salts, and fine silica mud doesn’t appeal to you, think again. Just about everyone who visits Reykjavik schedules a little time at the famous Bláa Lóniđ (Blue Lagoon), some of whom make it their first stop after deplaning from their overnight flight at Keflavik International Airport, about 15 miles away. But that doesn’t mean it’s a silly tourist trap — it’s a favorite with Icelandic folk, too, and it’s guaranteed to make a lasting impression. This geothermal spa owes its existence to a nearby geothermal plant that’s powered by superheated seawater drawn from deep bore holes in the surrounding black lava flows. After the steam passes through the turbines, big condensers convert it back into water, which is then channeled into a huge artificial lagoon with temperatures of about 100°F. I changed into my swim trunks and headed outside into a perfectly nasty spring day of frigid air, driving wind, and horizontal rain, and jumped into the steamy lagoon. From the neck down, I was amazingly warm and relaxed, but from the neck up, blowing rain pelted my face and nearly blinded me. Needing shelter, I hunted for and found a little protected cove, where, much to my surprise, I soaked quite comfortably in the salutary water for over an hour in a soothing mixture of elements that benefit one’s skin. Afterward, thoroughly warmed up and dried off, I treated myself to a wonderful lunch on the property: paprika soup and fillet of lamb with Dijon sauce and potato pancakes.

#2 Go Into — and Up — Hallgrímskirkja

With a few notable exceptions, Iceland’s capital isn’t known for its architecture. One of those exceptions is the astounding Hallgrímskirkja, an enormous Lutheran church atop a hill that took 41 years to build (1945–86). Designed to resemble the shapes created when lava cools into basalt rock (formations you’ll find around the island once you leave Reykjavik), the church features a tremendous circular apse topped with a bell-shaped dome, and staggered wings on either side of a soaring steeple. Extremely tall but relatively slender plain-glass windows permit light to flow into the austere all-white interior, not only conveying a sense of purity but also helping to focus attention on some of the cathedral’s few ornamental elements, like the Icelandic basalt and Czech crystal baptismal font, and the nation’s largest organ. An elevator whisked me up to the top of the 250-foot-tall steeple. A fierce wind on the outdoor observation level tossed me around a bit, but the 360-degree view was worth the tussle and provided a sweeping orientation to the city’s layout as well as the water and snowy mountains surrounding it.

#3 Fall in Love With Irresistible Puffins

You can’t help but be charmed by these adorable birds, and when I was aboard the Puffin Express’ Skúlaskeið, I was thrilled to see thousands of Atlantic puffins nesting on, floating around, and flying above Arukey island just outside Reykjavik Harbor. These black and white birds with colorful beaks, heartwarmingly sad eyes, and bright orange webbed feet look a little awkward in the air (like an airplane attempting to land on a blustery day), but they’re tremendous swimmers and can dive down nearly 200 feet to find food. Puffins live up to about 25 years. They’re monogamous throughout their lives and renew their relationships every spring at the same nesting hole. One of the best ways to observe them in their natural habitat is on this inexpensive hour-long trip that will sail you as close as possible to nesting colony islands — but binoculars or a strong camera lens will bring these endearing creatures even closer for your enjoyment. You’ll instantly feel happier.

#4 Contemplate the Outdoor Sculptures and Statues

All around downtown Reykjavik, traditional statues and modern sculptures mingle in a striking — and free — display of public art. The greatest concentration can be found in the sculpture garden outside the Einar Jónsson Museum. More than two dozen bronze casts of works by Iceland’s first sculptor range from a traditional statue of the leader of the Icelandic independence movement to his more interpretive realizations of dawn, fate, and grief. But the city’s great art is not restricted to the garden. For instance, in front of Hallgrímskirkja, you’ll find a 50-ton statue of Leif Erikson standing at the bow of a Viking longboat — a gift to Iceland from the United States on the 1,000^th anniversary of the Alþhing, the oldest continuous parliamentary democracy in the world (established in 930). Some of my favorites just popped up unexpectedly as I strolled around this open and low-rise city: the dramatic and undeniably Nordic statue of the Viking Ingólfur Arnarson; the Sólfar (Sun Voyager) sculpture — a stainless-steel dreamboat positioned, appropriately, right on the waterfront; and the Monument to the Unknown Bureaucrat, a male figure in a suit and carrying a briefcase, with his head, chest, shoulders, and upper arms entombed in a solid block of rock, that can be interpreted as a nod to faceless officials who make the world go ’round, or to how everyday life crushes down on ordinary people, or, if you will, to how most politicians are complete blockheads.

#5 Splurge on a Fine Dinner at Argentina

A steakhouse named Argentina hardly seemed like a traditionally Icelandic destination for dinner. But it turned out to be my best (and most expensive) meal in all of Iceland. Housed in an unassuming building, this phenomenal high-end steakhouse presents an evocative interior with lots of dark wood, brick arches, exceptionally comfortable leather seating, and the occasional steer horns above a doorway. Since opening day in 1989, Argentina has crafted a terrific menu, served by a seasoned staff (who inadvertently strike a comical pose as they tote around peppermills that are a good two feet long). I enjoyed a creative salad of fresh greens, tomatoes, blueberries, raspberries, and oranges, topped with a crispy wafer; beef tenderloin grilled over wooden coal with a light garlic sauce and served with wok vegetables and a baked potato with a light butter; and warm Valrhona chocolate cake with ice cream that took 20 minutes to prepare.

Five Runners-up

• Watch for minke whales aboard a boat in the North Atlantic.
• Take in the history in and around Austurvöllur, the city’s popular public square.
• Enjoy close encounters with the ducks, swans, and geese along a stroll around Tjörnin, a prominent lake in the city center.
• Partake in Reykjavik’s nightlife at a boisterous bar or an intimate lounge.
• Admire the camerawork of professionals at the Reykjavik Museum of Photography.