Trudge to the top of Copenhagen's Round Tower, one of the oldest and most imposing structures in the city's Old Town, and you will be treated to a view that is . . . well, a little uninspiring. Below you, a curiously unharmonious tangle of chimneys and church spires and copper-green roofs sprawls outward from the Old Town to a distant haze of suburban tower blocks, factories and shipyards. In the dull drizzle of a northern European winter, you won't be inclined to linger.

But return to the narrow streets below, most especially to that busy, aromatic, pedestrian-only artery called Stroget, and you will find yourself in one of the most agreeable and friendly capitals of the world.

God has never been especially generous to Copenhagen. First, he sited it on a tract of land as flat and featureless as a tabletop, and gave it a climate in which gray skies and dribbling rain play an all too prominent part. And then, as a final indignity, the city suffered three major fires in less than a century that left it bereft of almost all notable architecture.

But as compensation, Copenhagen was peopled with Danes. Other cities have great monuments; Copenhagen has great people. They are a friendly, easygoing lot, intelligent, prosperous (Denmark has the eighth highest per-capita income in the world) -- and so uniformly blond and good-looking that you begin to feel, after a day or two, like apologizing for being a little bit sloppy and dim.

The one thing the Danes have never been particularly good at is making history. Occasionally they will send a Roald Amundsen off to discover the South Pole or badger a Niels Bohr into devising a new theory of particle physics, and about once a millennium they will all get up from the table together and go off with a King Canute to conquer foreign lands. But mostly they are nonbelligerent, content to sit placidly in some public place drinking coffee or beer.

Even World War II was, for most stunned Danes, over and done with in less than a day. Hitler's tanks crossed the border under cover of darkness and had taken control of the country by dawn. Most people slept through it all. As a politician of the day remarked: "We were captured by telegram." (A rich and ironic sense of humor, it will be noted, is another Danish trait.)

A refreshing side effect of all this is that Copenhagen is free of any delusions of self-importance. The city has no monuments to an imperial past and, apart from the occasional palace and embassy, very little to indicate that it is a world capital. The whole feel of the place is almost determinedly provincial. In fact, this is a place where even the monarch, Queen Margrethe, can often be spotted mingling with early-morning shoppers in the Old Town. (When asked who guards her in such circumstances, a Dane will reply, "We all do.")

Copenhagen is home to 1.5 million people -- more than a quarter of the Danish population -- but it has the pace and ambiance of a university town (which, in fact, is what its Old Town mostly is). It is a city in which the morning rush hour lasts all of 10 minutes and the evening rush never quite gets going at all. (At the first sign of things becoming busy, everyone retires to a cafe' or bar.)

Hardly anyone wears a necktie or carries a briefcase or looks harried. The lack of a sense of urgency is underlined by the fact that the city's main thoroughfare is closed to cars. The Stroget, which loosely translates as "strolling place," is in fact not one street but five (Frederiksberggade, Nygade, Vimmelskaftet, Amagertorv and Ostergade) that run one into another for 1.2 miles between the city's two principal squares, Radhuspladsen and Kongens Nytorv. Confusingly, although everyone calls it Stroget, the name seldom appears on maps.

In any case, taken together, the five streets form one of the longest traffic-free streets in the world. It is also one of the liveliest and most agreeable, lined with cafe's, boutiques, banks and department stores. The more elegant shops -- Brodrene Andersen for clothes; Holmegaard and Royal Copenhagen for porcelain; Georg Jensen for silver and cutlery, and Illums Bolighus for the best of Danish furniture design and craftsmanship -- are clustered at its eastern end. Easily missed (but well worth seeking out) is Pistolstraede, a hole-in-the-wall passageway of elegant boutiques and restaurants just west of Ny Oestergade.

Copenhagen is emphatically a walking town. And as with many European cities, much of the best of the city lies tucked away in courtyards and down anonymous-looking passages, unseen by most tourists. Midway down Stroget, for instance, a cobbled lane leads past the old Church of the Holy Ghost. At the end, just beyond Jorn's Galleri , is an archway leading to a series of decidedly private-looking courtyards. Press on, ignoring the uneasy feeling that you will at any moment blunder into someone's kitchen, and you will shortly emerge in Graabrodretorv, or Grayfriars' Square, an ancient cobbled refuge of agreeable cafe's and well-weathered charm. It is a bit like stepping through a time warp.

Actually, Copenhagen, founded in 1167, is relatively young by European standards. Much of its architecture is even younger, dating from the late 19th and early 20th centuries. Individually, the massive, solid, rather anonymous-looking buildings that loom over the winding streets like hulking bodyguards often appear colorless and dull, but taken together they can give whole neighborhoods an air of subtle elegance.

Copenhagen is compact, another benefit for the walker. Most of the city's 40 public art galleries and museums (accommodating such specialized interests as toys, theater, history and medicine) are within an easy stroll of Stroget. The largest, lying just behind Christiansborg Palace (now the home of the Danish Parliament, or Folketing), is the National Museum (Nationalmuseet). On its three floors you will find a vast and often very beautiful collection of craftworks and artifacts from Danish history. Its Viking displays are the finest in the world. The whole is strangely overlooked, even by Danes; you may well have the place almost all to yourself.

Nearby is Copenhagen's other great museum, the Ny Carlsberg Glyptotek, founded by the famous brewing family and containing one of the most outstanding collections of Roman, Etruscan and Egyptian art in the world, plus a good assortment of Impressionist paintings.

But perhaps the most overlooked art museum in town -- indeed, one of the most overlooked in Europe -- is the Hirschsprung Collection in Oestre Anlaeg Park, just beyond the larger and more famous (and instantly forgettable) Royal Museum of Fine Arts. Assembled by one man over 40 years, the Hirschsprung Collection contains 884 paintings, mostly from the 19th century, all packed with fastidious care into 20 or so mostly small rooms. Almost all the paintings are light, airy and distinguished by good humor and simple themes. An enchanting place.

Copenhagen's compulsive joviality is vividly manifested in Tivoli, the famous amusement park in the heart of the city, which features 20 acres of greenery, gardens, lakes, theaters, dance halls and restaurants, all illuminated by more than 100,000 colored lights. Tivoli is a national institution, not so much a fun-fair as an oasis -- a place to pop into for coffee and a bite to eat several times a week rather than to romp through one day a year.

Eating in Copenhagen is never a problem. There are more than 2,000 restaurants and they appear, almost without exception -- at least in my experience -- to be excellent. Many of the best are to be found along Nyhavn, a three-block-long canal lined with narrow, gabled 17th- and 18th-century houses, looking for all the world like a piece of Amsterdam gone astray. (The neighborhood was in fact originally settled by Dutch sailors.) Among the best and friendliest of the street's dozen or so restaurants is Skipperkroen at No. 27. At the foot of the street is one of Copenhagen's most distinctive hotels, known simply as 71 Nyhavn, and housed in a large, carefully restored former warehouse. A tiny, though very comfortable, garret room there can set you back about $50 a night. But it is awash with character and the breakfasts (which are included in the price) are simply superb.

Nyhavn and its immediate neighborhood were once the haunt of sailors, and the area retains a certain raffish air. There are still a couple of tattoo parlors and the kind of bars through whose grimy windows you half expect to see Popeye and Bluto trading blows. But the street is being dragged almost forcibly upmarket and any sense of danger you may have is entirely illusory.

Copenhagen is, in fact, one of the safest cities in the world. Apart from a small area behind the central railway station where lavishly tattooed thugs hang out on street corners (and where this traveler wouldn't venture again without a howitzer), the city is safe for anyone at any time of the day or night.

What it is not, however, is cheap. One way to pare costs, and save some inconvenience into the bargain, is to get a Copenhagen Card (available from the main tourist office at 22 H. C. Andersens Blvd., or from hotels and travel agents). Copenhagen Cards are valid for one to three days and admit you to 36 museums, permit unlimited travel on buses and trains as far as Elsinore and give a 50 percent discount on ferry crossings to Sweden. The one-day card is about $6.50, two days $12 and three days $16; they are available from the Tourist Information Office in Copenhagen, the city's hotels and travel agents, and major railroad stations around the capital.

A more unconventional way to defray your costs is to bet your friends 50 cents whether the correct pronunciation is Copen-hay-gen with a long "a" or Copen-hah-gen with a short one. In fact, according to Kurt Nielsen of the Danish Tourist Board in Copenhagen (or Kobenhavn as it's spelled locally), the correct pronunciation, as nearly as it can be rendered into English, is Koopen-how-en.

That will be 50 cents, please.