Due to the crazy algorithm of flight scheduling, some airports are frequent purgatories for travelers in transit. But instead of squandering this downtime, think of it as a warm-up­­ to your main trip. To get you started, we’ve highlighted some diversions at several notorious long-layover airports. For more ideas, check the airport Web sites.

Frankfurt

Trains run between the airport and the city center; travel time to the main station is about 15 minutes. From there, catch a Hop On-Hop Off bus, which departs every half-hour. Jump off at Alt-Sachsenhausen, the district of traditional apple wine restaurants. To stretch your legs, walk along the Main River to the Roemerberg, the historic square with half-timber houses, the Fountain of Justice, a museum and more. The stroll should take no more than 25 minutes, so depending on your layover, you can complete several laps. Info: www.frankfurt-airport.com

Amsterdam

Holland Tours Schiphol, departing from the airport, offers various tours, including the canals, a windmill park and the Red Light District. If you prefer to go it alone, trains leave frequently from the airport to Centraal Station. Fan out by foot to Dam Square, home of the Royal Palace; Kalverstraat , a shop-happy pedestrian street; or such legendary institutions as the Rijksmuseum , the Van Gogh Museum and the Anne Frank House. For a watery excursion­­, don your sailor’s cap for a canal boat tour. Info: www.schiphol.com

Tokyo’s Narita

If you have a substantial time cushion, take the Narita Express into Tokyo, about an hour away. The train station houses a huge shopping mall and restaurants in the basement. Nearby, you can explore the Imperial Palace and the Mitsubishi Ichigokan Museum , an art institution that opened last year. For tighter schedules, stick closer to the airport and visit the Naritasan Shinshoji Temple, one of the largest Buddhist temples in the greater Tokyo area. (Take the Keisei Main Line, then a cab.) Shops selling traditional crafts, souvenirs and snacks border the route to the main gate. For a big dose of nature, skip around the surrounding Naritasan Park. Info: www.
narita-airport.jp/en

(ROBYN BECK/AFP/GETTY IMAGES)
Los Angeles

Hit the beach: Hermosa, Redondo and Manhattan are a quick cab ride from the airport. Or take a Metro shuttle from the airport and connect to a Beach Cities Transit bus. The FlyAway bus offers nonstop service between LAX and four destinations, including Union Station, within walking distance of Chinatown, historic Olvera Street and El Pueblo de Los Angeles Historical Monument; and Westwood/UCLA, which features a sculpture garden, the Fowler Museum and lots of green campus. Starline Tours picks up from the airport and ferries visitors around Hollywood, Beverly Hills and other star-studded locations. Info: www.lax.org

Miami

Even if your final destination is cold, throw a bathing suit into your carry-on. From the airport, cabs charge a flat rate to South Beach. Or catch the Airport Flyer express bus, which stops at 41st Street and Alton Road, one block from a quiet strand, and 16th Street, in noisy South Beach. The second stop is also near Lincoln Road, a strip of galleries, outdoor cafes, boutiques and peacock people. The shuttle’s last stop is the Earlington Heights Metrorail station. From there, head downtown and pop into the Miami Science Museum or the Vizcaya Museum and Gardens . Total travel time from the airport: about 30 minutes one way. For shopping and dining a little closer, mill around the Dolphin Mall , five miles from MIA. To relax before your real trip, grab a seat on Gray Line’s Hop On-Hop Off tour bus, which picks up at the airport and drives loops around the beach and the city. Info: www.miami-airport.com.