Saul Steinberg (1914–99) was a conventional illustrator who made unconventional illustrations. A poet of the street, his genius was not as a draftsman, per se, but, rather, as a storyteller, a punster, a town recorder, and a satirical documentarian. For Steinberg, who in many ways was a realist artist from the old school, Modernism, along with the whole 20th century, was a spectacle to be treated with skepticism and delight. And what better place to enjoy the hodgepodge bazaar of rapidly changing eclectic styles — artistic, architectural, and otherwise — than New York City at midcentury.

Steinberg, born and reared in Romania, studied architecture in Milan, Italy, where he was celebrated as a cartoonist. In 1942, he fled Fascist Italy and moved to New York, which was to become not only his home but his favorite subject for nearly six decades. Steinberg is best known as an illustrator for the New Yorker, which published more than 1,000 of his drawings and cover art, but he was also a creator of fashion designs, stage sets, sculptures, murals, greeting cards, and advertisements.

Three New York exhibits, at the Morgan Library and Museum, the Museum of the City of New York, and the Adam Baumgold Gallery, combined provide us with nearly 200 of Steinberg’s works. Together they give us a full, rich view of a man, his ideas, his wit, his wisdom, and his art; a man who has greatly influenced, if not greatly defined, how New Yorkers have collectively seen, appreciated, and laughed at themselves and their city for the last 50 years.

The Morgan’s show, a chronological retrospective that, like the MCNY exhibit, was curated by Joel Smith, is the largest, most diverse, and fullest of the three, but each show offers something worthwhile and unique. At the Morgan, the exhibit has been subtitled “Illuminations,” which is clearly an attempt to align Steinberg’s work with that of the medieval illuminators in the library’s permanent collection. This lowbrow/high-brow alliance, not unlike MoMA’s attempt last year to elevate Pixar’s animation to the level of art, is more than a stretch. It forces Steinberg to compete in an arena not only beyond him but completely other, which can distract from his inimitable gifts. The show, which might have been more appropriately installed at the Cooper-Hewitt or the Herb Lubalin Study Center of Design and Typography, is also a clear sign that the new Morgan is leaning toward shows with more mass appeal.

Be that as it may, Steinberg is brimming with mass appeal, especially to New Yorkers. No matter where you see his work, it stands on its own. Steinberg is not the Daumier of our time. He was extremely inventive, but he could not really draw that well, and often his captionless cartoons are visual one-liners — oh, but what great one-liners. His hand — wiry, lithe, cunning, and concise — was in tune with his eye, which was perceptive, good-humoredly critical, and often directly on target.

The most famous of Steinberg’s New Yorker covers, on view at the Morgan, is “View of the World From 9th Avenue” (1976), a perspectival map seen from Ninth Avenue in which New York’s buildings, automobiles, avenues, and people are clearly delineated. Beyond the West Side Highway we see a narrow strip labeled “Hudson River”; next to that is another narrower strip: “Jersey”; then a flat, green rectangle, bordered by “Canada,””Mexico,” and “Pacific Ocean,” with a few lumps of earth and landmarks such as “Nebraska,” “Texas,” “Washington D.C.,” “Las Vegas,” “Chicago,” and “Los Angeles.” In the far distance is a wavering strip on the horizon divided into “China,” “Japan,” and “Russia.”

The MCNY exhibit puts Steinberg in context. Placing his work next to maps, photographs, prints, advertisements, and illustrations from the 19th and 20th centuries, it establishes the breadth of Steinberg’s reach and of New York’s tradition of satire and illustration, a tradition from which he heavily drew and which he furthered. The show includes precedents for Steinberg’s work, including the lithograph “New York & Environs” (1859), an illustration of the earth in which Manhattan, dwarfing the rest of the world, is the size of the Asian continent.

Steinberg was immensely clever and diverse. Some of his most engaging pieces are false documents or certificates decorated with rubber stamps, gold seals, and beautifully illegible calligraphy, which he could churn our in various hands. Steinberg tackled the subjects of Hitler, Trotsky, and Hiroshima; matrons, hippies, and police officers. He did riffs on Cubism, Pointillism, Social Realism, and Neoclassicism. He borrowed or stole freely from folk art, Duchamp, Klee, Joseph Cornell, Léger, Baron Munchausen, Currier & Ives, Seymour Chwast, Picasso, Ingres, Alexander Calder, Walker Evans, and Barnum & Bailey; and he worked on other artists’ postcards and photographs. But in Steinberg’s best work, which is of New York, somehow he made the amalgamations all his own. In the end he created an art that feels as if, belonging to all of us, it is part of the greater fabric of our city.

Many of Steinberg’s works are laughout-loud funny. And his art is a veritable feast of styles and periods and of the constantly changing metropolis. Steinberg could also transform the city into fairytale worlds that are both dreamlike and threatening. In Steinberg’s hands, buildings, as if tired of staying in one place, uproot themselves and parade down the avenues, the Chrysler Building becomes a lavish ziggurat, and Lady Liberty is depicted as an angry American Indian.

In almost all of Steinberg there is a circus-like mix of the absurd, the insane, the comic, and the terrifying. His drawings of women turn Upper East Side matrons — with their sprawling furs, turned-up noses, tiny dogs, and exotic hats sprouting feathers and flowers — into strange creatures as familiar as they are frightening. In “Bleecker Street”(1970),Steinberg paints the city as a strange game board and crowded sideshow. A crocodile, a cop as knight on horseback, a police car as windup toy, numerous freaks and aliens and amalgams of every kind all walk the street, presenting themselves to us on the extroverted stage that is New York. The drawing resembles a crazily doodled page from an adolescent’s notebook — but that Dickensian page, in which all of us can be found if we look close enough, is not fiction. It is a quote directly from the book of our life.

The Morgan Library and Museum from tomorrow through March 4 (225 Madison Ave., between 36th and 37th streets, 212-685-0008);

The Museum of the City of New York until March 25 (1220 Fifth Ave. at 103rd Street, 212-534-1672);

Adam Baumgold until February 10 (74 E. 79th St., between Madison and Park avenues, 212-861-7338).