We arrive at Harry's Bar at one o'clock on a chilly, sunny January afternoon, pushing through the narrow saloon doors. Mario greets and leads us past the bustling little bar, dispensing its elegant prosecco-and-peach-nectar bellinis—a house invention—and its stiletto-blade martinis, to the banquette table at the end of the small downstairs room. This is the best seat in the house, though the two corner tables on either side of us are the super-A tables. At one, a well-dressed elderly lady pushes ravioli around her plate while her guests, a younger couple, devour steak tartare. At the other, a sportily-attired middle-aged couple orders chicken croquettes and croques monsieurs (long and thin and swathed in paper napkins).

Claudio, whom we'd met the day before moonlighting at the Palazzo Brandolini, takes our order for, well, a bellini and a martini. We are tempted by the croquettes and croques—Harry's is famous in knowing circles for such casual bar menu items—but ultimately we begin with a simple salad of very fresh little scampi and plump, sweet borlotti beans, and an order of pale, delicate carpaccio, crosshatched with a mayonnaise-mustard sauce the color of ivory. (This dish, which Venetians usually eat as a main course, was invented here only in 1950, and named after the great Venetian Renaissance painter Vittore Carpaccio, the subject of an exhibition in the city earlier that year.) Before our pasta course—homemade ravioli filled with ricotta and glazed with butter and soft little bits of cardoon—Claudio, as if he's afraid that we might miss something, brings us a tiny plate of simple boiled schie (ethereal miniature gray shrimp from the lagoon) and a bowl of hearty pasta e fagioli, the bean soup that is Venetian soul food. Our main course is fegato alla veneziana, almost certainly the best in Venice—crisp-edged morsels of calf's liver and rings and strands of caramelized onions. We forgo dessert. But as we sit there, in the simply but warmly furnished, sunlit dining room, finishing our Loredan Gasparini Venegazzu, a silky red from the hills 25 miles northwest of Venice ("That's the Contessa Loredan," whispers Claudio, nodding at the elegant elderly woman at the corner table), life seems very sweet indeed.

We've had other experiences at Harry's Bar, of course—lots of them—and they haven't usually involved a prime downstairs table and little extras from the waiter (though there's often been a countess or two around). But never once—even when we were young, alone, and relatively impecunious—have we ever been condescended to or treated rudely; and, however heart-stopping the tariff might have been, never once have we walked away feeling that we haven't gotten more than our money's worth.

Harry's Bar in Venice was not the first famous establishment to bear that name. The honor goes to the bar that took that name in Paris in 1917. This Harry's Bar dates from 1931: One Giuseppe Cipriani, a bartender at the Hotel Europa in Venice, had loaned money to a dipsomanaical young American habitue named Harry Pickering. Pickering used the loan to go back to the States, but returned with Cipriani's lire and more—enough to bankroll a bar, which the two named Harry's. Over the years, while remaining one of the world's great watering holes, Harry's developed into a first-rate restaurant, too. Other Harry's Bars around the world—and they are legion—have no relation to the Cipriani original and are related only tenuously to each other, if at all. The Cipriani family, however, now also owns the casual Harry's Dolci on the Venetian island of Giudecca, three restaurants in Buenos Aires, and three restaurants and several banquet spaces in Manhattan.

Serious restaurant critics sometimes criticize Harry's Bar and its offspring, complaining that the food is too ordinary and the surroundings too casual to merit such high prices. But "ordinary" food in a casual setting is precisely what Arrigo Cipriani—Giuseppe's son and now the patriarch of the family, intends. "The service should be simple in good Italian restaurants," he tells us one day, "and Italian food should have a home taste. In the best Italian restaurants, the food doesn't taste like restaurant food."

"It was a scandal when Giuseppe Cipriani first served fegato alla veneziana at Harry's Bar," says Natale Rusconi, director of the Hotel Cipriani on the Giudecca, as he offers us another kind of Italian food with a "home taste" at his little jewel of a house facing the Giudecca, on the south flank of Venice's Dorsoduro quarter. "It was a very daring thing to do; the start of a new Italian cuisine when all the grand restaurants still had French menus." It is clear that he greatly admired Giuseppe. Of Giuseppe's son, Arrigo, on the other hand, he says only that "He is … special." (This is not meant as a compliment.) Cipriani is far less oblique in his assessment of Rusconi: In Harry's Bar: The Life and Times of the Legendary Venice Landmark (Arcade, 1996), he describes him as having "a liking for old recipes modernized to guarantee acidity; and an almost incestuous love of his own ego." The two men are, in other words, Venetian don't-invite-'ems.

The point of contention between Cipriani and Rusconi is the Hotel Cipriani, the luxurious hostelry opened in 1958 by Giuseppe Cipriani with the backing of Lord Iveagh, owner of Guinness, the Irish brewery. After Iveagh's death in 1967, Guinness decided to sell the hotel. The Ciprianis had a backer willing to buy it, but it went instead to Sea Containers, a massive shipping company run by Kentucky-born James Sherwood. Sherwood, whose sensibilities are clearly foreign to Cipriani, installed Rusconi, a veteran hotelier who had once managed Venice's famed Gritti Palace. Sea Containers and the Ciprianis have feuded ever since.

We certainly can't imagine Arrigo Cipriani—who assiduously maintains an aesthetic distance from his customers —inviting us home for tripe with vegetables, as Rusconi has done. We arrive early to help in the preparations (he apprenticed in the kitchens of the Savoy Hotel in London in 1954, he tells us, and turns vegetables like a pro). In Rusconi's garden, we sip prosecco, nibble air-dried beef, and then tuck into steaming plates of earthy, intensely savory tripe stew. It is an old recipe, unmodernized, unacidic, impeccable.

Our last day in Venice, in June, is a Cipriani day. At lunchtime, we relax on the gorgeous terrace of the Hotel Cipriani. The Biennale has just opened, and there are celebrities right and left (we see Steve Martin pay his respects at Lauren Hutton's table) as we devour pasta e fagioli and heaps of lightly fried scampi and calamari—superb but modest Venetian dishes in elegant surroundings. At night we're back on the Giudecca, at Harry's Dolci, with Brandino and Marie Brandolini, eating vitello tonnato and gratineed tagliolini. There is Biennale spillover here, too: The legendary, octogenarian American decorator Tony Duquette presides over a large table; Vogue correspondent Hamish Bowles stops by our table. And as the sun sets, we notice Arrigo Cipriani himself, not working the door but sitting calmly, in a pale yellow suit, drinking bellinis with his wife, Tommasina, paying attention only to her.