LAST WEEK NBC's "Today" show came to Washington and after showing viewers a panoramic vista of a sparkling green Mall and the splendor of the monuments offered this grim assessment of what is really happening behind the glossy postcard image: a city with a mayor accused of smoking crack and the dubious honor of being the "murder capital of the country."

"Washington's problems just won't go away," said "Today's" Katherine Couric. "Look at some of the headlines that appeared during two weeks in May. Mayor Barry indicted on more cocaine charges. American University President Richard Berendzen pleads guilty to obscene phone calls. Four Washington hockey players accused of rape. Police warn visitors away from Georgetown. Welcome to the nation's capital."

The "Today" show is not alone in describing the city as the modern world's Sodom and Gomorrah. The National Rifle Association is running television spots featuring actor Charlton Heston praising the right to bear arms as he explains that he is walking through one of the most dangerous places on earth -- just as the Capitol dome comes into view in the background.

The Independent of London recently ran a story about the mayor's race that focused on one minor candidate, a prostitute who bragged that local politics and the city in general are full of "whores." In Bogota, Colombia, newspapers run daily stories on the Barry drug trial and drug murders in this area. The managing editor of El Tiempo, Colombia's largest circulation daily, told a reporter last week that Washington and its mayor are an international "symbol of how hypocritical U.S. society and {its anti-drug} policies are."

From these stories and the psychological baggage left over from Richard Nixon's assault on the city's image as the "crime capital," it is easy to imagine that Washington is a horrible place to live. And in some ways it is: The Beltway is Hell itself, the summers are steamy and there's no baseball team. But as most of us who live here will affirm, Washington -- and even more so the Washington suburbs -- are a great place to live. The best proof we can offer is that people keep coming here and staying. Though the Distict's population has steadily dropped since the 1950s with the departure of middle-class white and black families, those people have gone no farther than the city's suburbs where the population has ballooned -- the area added 400,000 people in the '80s. Even in the District, despite its high housing prices, high taxes, poor services, troubled schools and political scandals, the number of young people seeking urban living is actually increasing.

When those young people start marrying, having children and moving to the suburbs, they will, as those before them, still see themselves as Washingtonians, happy to be in this area. Even if they decide to stay in the city they will not find themselves in the place described in the headlines. Sure, the city has an eroding tax base and mounting demands for services, but compared with other big central cities it has the second lowest rate of violent crime, the lowest rate in forcible rape and robbery, the third lowest unemployment rate and the lowest poverty rate.

"If you compare the District to other major central cities for jobs, for crime, for quality of living generally, it actually looks very, very good," said Atlee Shidler, president of the Greater Washington Research Center. "People move to Washington from Oklahoma and California and most of them stay in the area for the rest of their lives."Even government haters find the capital area hard to leave. As columnist Michael Kinsley recently wrote, for all the "alleged distaste for Washington" among staunch conservatives, about two-thirds of the top officials in the Reagan administration stayed here when Reagan went west.

People from around the world also find Washington an exciting, comfortable place to live. "Many people from the Caribbean community came here to study at Howard and never went back," said Wesley Kirton, editor of the Caribbean Sun newspaper published in Falls Church. "Other members of the Caribbean community they meet here are well educated, well-to-do. Washington is a pretty place with lots of wide open green spaces . . . . It's not too cold. For people with a high level of awareness of world politics being here helps keep them abreast of what is happening globally."

Employers stay here, too. When the Greater Washington Research Center asked major employers if cutbacks in federal contracting might prompt them to leave the area, more than half said they would not consider leaving because of the quality of life and business opportunities outside government.

"In other words, they like living here," said Shidler.

"Quality of life to these corporations means that in the Washington area you can go from the seashore to the mountains, there is a high level of culture and sports activity, and no one else has the Smithsonian, the Kennedy Center and all the theaters," said Robert Grow, deputy director of the Washington-Baltimore Regional Association. So why do outsiders love to hate Washington? One reason may be that the city's image is largely a mirror of national anxieties.

"Washington has always been a surrogate for whatever is the great national concern of the moment," said Steven Diner, professor of history at George Mason University. "If you look back to the Reconstruction period after the Civil War, the city came to represent the question of what the government was going to do about black people -- make them full citizens of the republic or something else. In the 1950s Washington was portrayed in terms of civil rights. If you were for integration it was the 'Miracle City.' If you were against desegregation it was the 'Disaster City,' as whites left the schools. In the '60s, Washington was the city that represented the urban crisis and riots within blocks of the White House. In the '70s, Washington was the city of rich bureaucrats and yuppies feeding at the federal trough. And now Washington is the exemplar of municipal corruption and a drug-ravaged community."

But despite the negative imagery the Washington area stands out as a leader among the world's best places to live. A big reason is that the area is full of smart, successful people. Even the dullards are ambitious, conniving and well-connected. In fact, the Washington area has the highest concentration of educated adults in any major American area, according to census data -- twice as many adults here have college degrees as is true nationally.

Not surprisingly, local politicians are big boosters. "I like the people in this city," said William Lightfoot, the at-large D.C. Council member and lawyer. "The people are bright. There are tensions but race relations here are better than in Philadelphia {his hometown} and it is not violent. People tend to be friendly and it may sound corny but there are a lot of tree-lined streets and lovely homes. It's nice to live here."

Others agree. "My daughter is 20 years old and away at Columbia in New York and we were talking the other day about where she will settle down and have kids," said Goldie Rivkin, of Rivkin Associates, an urban planning firm in Bethesda. "And she was talking about taking the kids to the Smithsonian and doing other Washington things. I told her that her career might take her to some other city. She said she wouldn't go. She wants to stay in Washington. She said there is no better place to live."

And Rivkin's daughter will probably be able to stay here and find a job because the area has the highest rate of working women in the nation (67 percent) and is tops in the percentage of professional women in the work force. And the job she finds will probably be well-paid: The Washington metropolitan area is now the nation's most affluent with the highest percentage of affluent families and an average after-tax household income of around $49,000. And most of the area's jobs are good ones -- 72 percent are white-collar, more than 20 percent above the national average. Income among blacks is the highest of any major metropolitan area nationally.

"If I was a young man starting out," said former D.C. mayor Walter Washington, "and I don't care where I was born, I'd be on the fastest thing going to get to Washington."

Juan Williams writes regularly on politics for Outlook.