In this unseasonably warm season, there will surely be more sunny, brisk days when staying indoors feels stale and the city beckons to be seen. Such days call for a winter saunter. One of the best places for such an excursion is Madison Square.

Without public events and with the Shake Shack shuttered, the park is all but empty, which leaves a New York walker feeling as though he possesses the square. Within a compact compass, he can see more great buildings and outdoor artworks in 30 to 45 minutes than in any other comparably sized part of the city. And in this neighborhood, nearly every corner boasts a warm, noteworthy restaurant in which to revive afterward.

A winter walk should begin with appreciation for the skylines around Madison Square. Winter’s lack of foliage offers unobstructed urban vistas, which makes the season beloved by photographers of buildings. Along the east side of the square stand three classic New York skyscrapers. At the southeast corner of Madison Avenue and 24th Street, the Metropolitan Life Insurance Co.’s tower annex was the world’s tallest building when it was completed in 1909. Designed by Napoleon Le Brun & Sons, it’s one of Manhattan’s most distinctive skyscrapers, modeled after the Campanile of St. Mark’s in Venice. Not coincidentally, MetLife was garnering golden publicity by helping to restore the Campanile after it was damaged in a storm. The MetLife Tower has been converted to condos (increasingly the fate of our classic office skyscrapers, which resist retrofitting for the high-tech requirements of modern businesses), and its exterior has been sparkling restoration. The nighttime lighting of the fourfaced clock at the top is not to be missed.

Across 24th Street to the north is another former MetLife annex, a would-be world’s tallest building that was cut short, literally, by the Great Depression, ultimately rising only about one third as high as planned. Now the Credit Suisse First Boston Building, the art deco beauty, designed by Harvey Wiley Corbett and D. Everett Waid, occupies a full square block and was built in phases between 1929 and 1950.

To the north, between 26th and 27th streets, rises the majestic New York Life Insurance Company Building, designed by Cass Gilbert and built in 1928. The building’s golden pyramidal crown is the familiar symbol of New York Life. Unfortunately, the public no longer has access to the through-block lobby.

Diagonally across the square, at 23rd Street where Fifth Avenue and Broadway cross, stands the Flatiron Building, designed by D.H. Burnham & Co. and built in 1902. For some strange reason, many people think this was the first skyscraper in New York. It was far from that and was never even the tallest building in the city. But it is undeniably dramatic.

The buildings around the square are majestic, but the sculpture within the square is equally so. The oldest sculpture in the park is the seated bronze figure of Governor Seward, facing the northeast corner of Broadway and 23rd Street. It’s by Randolph Rogers and was dedicated in 1876. The oft-told story that Rogers placed Seward’s head on a casting of a Lincoln figure the sculptor had done is patently false. We are blessed with fine statuary to inspire us to contemplate the deeds of great men, not silly stories of a sculptor’s purported chicanery.

To the east, near Madison Avenue and 23rd Street, is a beautiful bronze statue of Senator Conkling, from 1893, by the great sculptor John Quincy Adams Ward. Across the square to the north, near Madison and 26th Street, is Chester A. Arthur in bronze from 1899, by George Bissell. The 21st president of the United States lived for many years nearby, at Lexington and 28th, in the building that is now Kalustyan’s, an Indian grocery.

The Appellate Division courthouse, at Madison and 25th, combines great architecture and great sculpture. Built in 1900 and designed by James Brown Lord, the courthouse’s sculptural program depicts a multicultural panoply of legal symbols and personages that belies quaint notions about past ignorance of non-Western cultures. Henry Hope Reed called this building “the epitome of the Beaux-Arts.”

Finally, just in from 26th Street, midway between Madison and Fifth avenues, stands the monument to Admiral Farragut, the first public commission executed by America’s greatest sculptor, Augustus Saint-Gaudens. The standing figure, in bronze, bespeaks fortitude. We have no trouble believing this is the man who said “Damn the torpedoes, full speed ahead!” The elaborate exedra — a sculptural base incorporating a bench for sitting — was co-designed by Saint-Gaudens and his friend Stanford White. The monument was unveiled in 1881. Look in the pebbled foreground for the bronze crab inscribed with the names of Saint-Gaudens and White.

And while Delmonico’s is no longer across the street at Fifth Avenue and 26th Street, you won’t want for good food and drink nearby.