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Start with an unbeatable art world doubleheader--a visit to the Frick Collection followed by a jaunt through the Chelsea gallery district. Inside Henry Clay Frick's beaux arts mansion, 18 galleries of Western art are home to three works by Vermeer, as well as paintings by Degas, Rembrandt, and Gainsborough; then there's what I think of as the "Fun With Fragonard" room. It's a compact, heady spin through the masters.

A world away, though only on the other side of the island, is the headquarters for contemporary art in New York: Galleries by the score have made their homes over the last few years on the less and less gritty blocks of far west Chelsea. There are major galleries, including Gagosian, Matthew Marks, Sonnabend, and Paula Cooper, but rather than seek out particular ones, I like to wander through the byways. That means exploring vertically--many galleries are tucked upstairs in nondescript buildings.

The city has always enthusiastically put out the welcome mat for musicians, and few have been more welcome than Louis Armstrong. Since last fall, Armstrong's Corona, Queens, home has been open to the public. He and his wife, Lucille, lived there for decades and you'll find original furnishings, his reel-to-reel recorder, and one of his gold-plated trumpets, all suffused with Satchmo spirit.

Spirit of an entirely different sort is in evidence nightly at Don't Tell Mama, a piano bar and cabaret in the Theater District. There's no telling what to expect--a musical revue, a cabaret singer, or a Judy Garland impersonator. Joe's Pub, adjacent to the Public Theater in the East Village, is named for the theater's late founder, Joseph Papp. Joe's has perhaps the most exciting roster of singers, musicians, comedians, and assorted offbeat acts anywhere in the city.

Crazy ideas somehow work in New York, and listening to chamber music on a barge on the East River is among the craziest. Yet Bargemusic is an absolute treat! Audiences listen with rapt attention to world-class musicians while staring out the window at a view of the Manhattan skyline; as music fills the room, the old barge sways and creaks.

After such subtle sophistication, the new Times Square is a sensory overload. Take in a Broadway show by all means, but don't overlook the more intimate off-Broadway theaters. Playwrights Horizons (which sent I Am My Own Wife over to Broadway, winning the 2004 Tony Award for Best Play and Best Actor) always seems to be up to something interesting. You may catch a work from a rising star playwright or even a musical. The first preview of each production has a limited number of pay-what-you-can seats.

If you have children in tow, Broadway shows may be too expensive, too long, and not geared to their ages. That's where the New Victory Theater comes in. All shows are meant for kids and their families, running times tend to be on the short side, and the top price is $30. Best of all, productions are generally first-rate. Kids will also have a blast at the American Museum of the Moving Image, in Astoria, Queens. Despite the fancy name, this is a fun place for all ages. There are interactive exhibits, screenings, and a collection of costumes and props that includes the chariot from Ben-Hur.

Central Park, which turned 150 in 2003, has never been more beautiful, and it maintains its considerable charms in all seasons. But the big news comes from the string of parks that have sprouted up  along the Hudson River  in the past few years. They start at the southern tip of Manhattan with Wagner Park--from which you can admire the Statue of Liberty and Ellis Island--and continue northward, jutting occasionally onto reclaimed piers. It's still a work in progress, but eventually the parks will extend all the way to Riverside Park on the Upper West Side. Walking along the Hudson, you'll see people of all shapes, sizes, and colors enjoying the city we've all come to appreciate ever more ardently.

Going to Ground Zero, where the World Trade Center towers stood, is a pilgrimage for many visitors. The rebuilding is now under way and visible from the viewing area, but also be sure to stop into St. Paul's Chapel--miraculously unharmed in the tragedy--directly across from the WTC site. In the weeks following the disaster, rescue workers and cleanup squads found refuge at the chapel. A permanent exhibit recounts those days.

A stroll away, in Battery Park City, is the Skyscraper Museum . It's a fascinating exhibit, irresistible to anyone who loves cities. Even if we all know that no city can possibly compare with this one.