LONDON — Straining for position, the runners pass the Olympic stadium and the aquatics center, sprinting through the damp gray of an East London morning in their brightly colored Lycra to the finish and the Podium beyond.

Not the medal podium. A café called the Podium, where the competitors in this monthly amateur 10K reward themselves with coffee and croissants.

Queen Elizabeth Olympic Park, the site of the 2012 London Olympics, is a surprisingly busy place. In addition to this 10K, there’s an international track cycling championship underway. The stadium is in the final stages of being converted into the new home of the soccer team West Ham United. The London Lions basketball team plays here, too, and there are public boot camps, yoga classes, circuit drills, and walking trails. From its observation deck, the 380-foot looping red steel tower built for the Olympics called the ArcelorMittal Orbit offers panoramic views of all of London and the world’s longest, fastest tunnel slide.

“There’s a lot that goes on in the park,’’ said Lizzie Pillinger, one of the runners, catching her breath after the 10K. “When the weather’s good, it’s really nice, with people out on the grass.’’

Still upset that Boston turned its back on hosting the Olympics? Not taking the corporate jet to Rio to enjoy the summer Games in person? The next best thing may be visiting the world’s Olympic venues, iconic and familiar places that are becoming destinations in themselves.

Some are as close to home as upstate New York.

“Our visitation always swells right during the Games or directly after, because it’s fresh in people’s memories,’’ said Alison Haas, director of the Lake Placid Olympic Museum, which commemorates the two winter Olympics held in that small New York village. “If you can somehow capture that Olympic spirit by going to visit a town or a city where an Olympics were held, it’s this special thing.’’

The museum recounts the “Miracle on Ice’’ game played at the 1980 Olympics in Lake Placid at which a young Team USA upset the unbeatable Soviet national hockey team, with a display that includes US goalie Jim Craig’s pads and jersey. It also tells the stories of the gold medal won there at the 1932 Games by 16-year-old figure skater Sonja Henie, and the five golds taken home by speed skater Eric Heiden in 1980.

Like Queen Elizabeth Olympic Park, Lake Placid banks on more than just nostalgia. Its Herb Brooks Arena, named in honor of the Miracle on Ice coach, hosts international hockey and figure-skating competitions and summer ice shows, and there is public skating year-round, including a summer figure-skating program.

You can also skate all year on the speed track from the 2002 Games in Salt Lake City, tour the stadium built in 329 BC in Athens that was used again for the first modern Olympics in 1896, visit the 1952 Helsinki sports arenas that have been converted to the Sports Museum of Finland, and watch an Atlanta Braves game at what you may recognize as the Centennial Olympic Stadium — now Turner Field — from 1996.

There’s public swimming in the summers in the Piscina Municipal de Montjuïc, the outdoor pool on Montjuïc Hill in Barcelona built for water polo over which also towers the high-diving platform that was by far the most memorable symbol of the 1992 Games there, made famous to a new generation as the backdrop of a Kylie Minogue video.

The nearby Anella Olímpica, or Olympic Ring, is where the rest of Barcelona’s Olympic venues are, including the Torre Calatrava, a broadcast tower that also serves as a giant sundial and was designed to look like an athlete holding the Olympic torch. Its base is decorated with the same kind of mosaic tile as in the works of modernist architect Antoni Gaudí.

The Olympic Ring — it’s also called the Parc de Montjuïc — is a comparatively quiet getaway, though still used for major sporting events and concerts. When those aren’t going on, the Olympic Stadium is open for tours, and the nearby Olympic Marina, another legacy of the Games, has become known for its seafood restaurants overlooking the ocean.

Barcelona also has a small Olympic museum like the one in Lake Placid. There are 26 Olympic museums worldwide, many of them in cities that have never hosted an Olympics. The largest is in Lausanne, Switzerland; the newest, scheduled to open in 2018 in Colorado Springs, where many Olympians train.

The Los Angeles Memorial Coliseum, home of the 1932 and 1984 summer Games, is planning a museum and just launched guided tours. But Joe Furin, its general manager, said many visitors are happy to just gaze at the field or look at the plaques memorializing athletes, coaches, and public figures who competed or appeared here: Knute Rockne, Babe Didrickson, Jesse Owens, Jackie Robinson.

“They’re walking where their heroes walked,’’ said Furin. “We have even more of that with international visitors, who watched their countrymen compete in 1984 and say, ‘I had to see the place I saw on TV.’ It’s that link to history.’’

There’s more to do than gaze, though, at newer Olympic venues that were meant to justify their huge costs by remaining useful.

Few are as ambitious as the Beijing National Stadium, the “Bird’s Nest,’’ which hosted the 2008 summer games and has become so much of a Chinese landmark that it’s a stop on tours that also visit the Great Wall.

The $423 million stadium is still used for athletic competitions and, in the winter, is filled with snow for a popular indoor festival that includes ski jumping and ice skating. The neighboring National Aquatics Center, or Water Cube, which hosted swimming and diving, has been converted into an enormous water park.

There’s a flurry of construction around the 560-acre Queen Elizabeth Olympic Park, too, where offices and homes are planned, along with a $1.9 billion cultural quarter called Olympicopolis that is to include the first overseas branch of the Smithsonian Institution and an offshoot of the Victoria & Albert Museum, plus shops, restaurants, and theaters. And what is billed as the world’s longest slide now hangs from the ArcelorMittal Orbit.

The park has already had nearly 10 million visitors since it opened a year after the Olympics.

“They’ve got the chance to swim in the Olympic pool, to ride their bike in the Olympic velodrome or the track outside,’’ said David Edmonds, chairman of the development corporation that oversees the site. “From this year they’ll be able to watch a football match’’ in the 60,000-seat stadium.

When fans poured back for the Rugby World Cup in the fall, he said, “You could hear them talking about what they had seen during the Olympics. There is still that kind of spirit, just from seeing the stadium, seeing the pool, walking across the bridge. Four years out, people coming to the park are still remembering the legacy of the Olympics.’’

Jon Marcus can be reached at jon@mysecretboston.com.