New York ? During a brisk morning ride on the New York City subway, the average commuter heading to work might not even bother looking out the train window.

But the nonchalant commuter’s loss is the savvy tourist’s gain. Visitors can take an extraordinary tour of New York — complete with panoramic views, music, art and even food — without ever leaving the subway system. And there is no better time to let the trains act as your guide than this fall, when New York observes the subway’s centennial. Of course, the nickel fare riders paid when the first trains ran on Oct. 27, 1904, is long gone. But at $2, it’s still the cheapest way to get around New York.

The 722-mile lifeline, which carries 7 million people daily, is also relatively safe and clean.

But it takes a daylong, crisscrossing trip on the trains to understand that, and to take in all the subway has to offer.

Get elevated

If you’re looking for music, you’ll most likely find it in busy midtown Manhattan stations. Some performers are sponsored by the Metropolitan Transportation Authority and have official “Music Under New York” signs, like the trio of young women who often play classical strings near the turnstiles at the Rockefeller Center stop. Others just show up, impromptu, with a guitar, drum or accordion and put on shows between the noisy trains’ arrivals and departures.

For the best views, however, you’ll need to leave Manhattan, where the system is largely underground, to access the elevated lines. Start your trip on an early autumn morning, taking the D train across the Manhattan Bridge, where you’ll be greeted by the sight of its better-known cousin, the Brooklyn Bridge. A 7 a.m. sunrise shimmers over the East River, and looking south through the train windows, you’ll be saluted by the Statue of Liberty, four miles away. To the north is the familiar Manhattan skyline, anchored by the distinctive Empire State Building and Chrysler Building.

Queens treasures

But a ride over the East River isn’t the only spectacular view a subway trip offers.

Sun sets on the New York City skyline as a subway train crosses Jamaica Bay en route to Far Rockaway in Queens, New York. Riders on the A train can watch planes take off and land at nearby John F. Kennedy International Airport.

Far on the eastern portion of Queens, the A train begins its 31-mile run, but not before passing two of the city’s most interesting landscapes.

First, it takes a 10-minute ride through the Jamaica Bay Wildlife Refuge, a marshland where swallows and egrets can be spotted along with plants and wildflowers that would commonly be found anywhere but New York.

From there the A train heads to John F. Kennedy International Airport, which displays a continual ballet of arriving and departing aircraft over the Atlantic Ocean-fed Jamaica Bay.

Transferring from the A to the Manhattan-bound L train at the Broadway Junction stop, riders get an aerial view of Brooklyn rooftops as the train winds and twists like a roller coaster on a 50-foot high elevated track. The next two stops offer views of historic Evergreen Cemetery, which boasts the graves of celebrities like Bill “Bojangles” Robinson and Tony Pastor, the father of vaudeville.

Once the L goes back into the tunnel, transfer to the Queens-bound G train at Metropolitan Avenue. At the last stop, Long Island City, change to the Queens-bound No. 7, which also runs above ground. Look for the Citibank skyscraper; at 48 stories, it is the tallest building in Queens. Its green glass exterior acts like a mirror, brightly reflecting sunlight around the neighborhood. Nearby (at Jackson Avenue and Crane Street) you can see a building known as “5 Pointz”; its walls are covered with graffiti, the tags of urban Picassos from around the world.

As the No. 7 continues eastward, passing through the diverse neighborhoods of Woodside, Jackson Heights, Corona and Flushing, it earns its nickname as the “international line.” Here you’ll find riders speaking everything from Spanish to Pakistani Urdu to Korean.

Soon the train passes by Flushing Meadows Corona Park, Queens’ largest public park and home of the Unisphere, the biggest globe in the world. The hollow steel structure, 120 feet tall, was erected for the 1964 World’s Fair.

During baseball season, as the train nears Shea Stadium, it is often filled with Mets fans in their blue caps and Piazza jerseys; you’ll also notice low-flying planes here, headed to and from LaGuardia Airport.

Grand Central views

Junior Mota, left, watches as Christian Mota, center, and Jimi Padilla play a game of chess while a nearby subway train travels an overhead pass in Ridgewood, Queens, New York.

The train continues into Flushing and winds up underground, emptying at the last stop. By now, it’s afternoon; stay on the No. 7 and double back into Manhattan, where you can change to the No. 4 train at Grand Central, the city’s most famous station and one of its busiest.

Back on the uptown or Bronx-bound No. 4 running along Manhattan’s Upper East Side, you’ll find examples of the system’s underground artwork. At the 59th Street station, the underpass displays Elizabeth Murray’s colorful glass mosaic called “Blooming,” which covers the walls with bright red trees, coffee cups and blue backgrounds.

In the Bronx, the No. 4 train eventually emerges aboveground for a view of the familiar blue bleachers at Yankee Stadium at 161st Street and River Avenue. Get off here and wind your way back to Manhattan via a series of transfers that will make you feel like a real New Yorker: Take the D to 145th Street, then head back uptown for just a couple stops, to 168th Street, where you can switch to the downtown Nos. 1 or 9.

Around 6 p.m., the window of the southbound No. 1 train from northern Manhattan affords what may be the subway system’s most dramatic view: The sun setting over the Hudson River and behind the hills of New Jersey, with urban Harlem in the foreground.

Then the train goes underground again, past the welded-steel throne sculptures at the 116th Street station (Columbia University), the Alice in Wonderland mosaic at 50th Street and “The Return of Spring” mural at Times Square.