CAN YOU believe it? We're the Cinderella of cities.

We're Number Two in the country in "desirability." Skip quickly over Atlanta being Number One -- that could ruin it for you. Hold on to the thought that the city of exiles is the second nicest place in the United States to live.

Yes, dear old Washington, the town America loves to dump on, is on the charts now as a cool place. The Big Apple barely noses us out in the arts; we're fifth in transportation. At our Kennedy Center last Monday night, you could hear Philip Smith play the Haydn Concerto for Trumpet and Orchestra in a way to call the dead from the grave. Any day, you can take our Metro and get where you're going by the time you've found a seat. Not- so-Big Apple, eat your heart out.

Can we can handle success? The question leaps to mind in the Shrink Capital of the World. We have more psychiatrists per capita than any area on the planet. Angst is our growth industry, second only to the advanced paranoia which afflicts all levels of government service, from the Oval Office to the Pentagon janitors' locker room. The president believes the Libyans are out to get him. The janitor broods that the president will get his job.

But that has been in the air since the John Adamses moved into the White House. From the first, the image of the Federal City has been that of a swamp -- a breeding ground of rogues, parasites and bad ideas. The rest of the country believes that the reason people living in Washington have massive recourse to Freud is that they live in Washington -- and are guilt-ridden for the part they play in squandering money, filling the Congressional Record with hypocritical blather and strangling honest businessmen with regulations and paperwork.

But now we are desirable. What do we do? Booster buttons? But what will be the symbol of our scientifically established fair city? A cherry tree? Some congressmen from Michigan would scream that we were pushing Japanese cars. The Washington Monument? Not since the day of the big government shutdown, when they locked the doors. Bad vibes for bureaucrats. We'll have a study commission with three retired generals, four California tennis players and a deadline of 1990.

The accolade comes at the best possible moment. We have just been advised of a "seasonal wave" of robberies and muggings. The first four days of 1982 brought 68 robberies, thefts and muggings, an indication that came too late for our surveyors and showed that, while more cultured, we are not necessarily more civilized. But we know we beat Atlanta in the PR of the thing. In Atlanta, scene of many child-murders, travelers see billboards with crime figures inscribed on them. It had something to do with a feud between state and local police. We have no such vulgar displays. We are not a state. In fact, we've never been sure what we are beyond a butt for politicians' jibes.

The initial local reaction to our new status was one of total surprise followed by a certain moroseness. We get the glass slipper -- well, the second pair anyway. We don't break out the champagne. We decant the doubts. How was the survey made? How large was the sample? Could any rational survivor of a Washington summer credit the "favorable" grade on climate? Did the authors, Richard Boyer and David Savageau, do any on-site inspection in mid-July? Were they using the humidity rate in Kuala Lumpur as their baseline?

Said a Washington woman who secretly loves the city: "I bet they holed up in the Library of Congress, where they got more data than they knew what to do with, in the middle of October, and went to lunch at the Jockey Club. I don't think we've heard the end of this."

Betimes, can Washington adjust? Will its inhabitants miss the hostility that enveloped them whenever they ventured out into what the First Citizen of the city invariably reminds them is "the real world?"

Will we be able to hold up our heads in say, Cleveland, Ohio, and proudly proclaim that we come from a city that used to be an expletive?

A senator from Oklahoma named Mike Monroney gave the ultimate rejoinder to our detractors. He said of the lawmakers, who had mortgaged their fortunes and their family life to finance the chance to come and live here part of the year: "They never go back to Pocatello."

But that was many years ago.

Until we got the results of the survey, we hadn't realized that anyone had noticed how beautiful we are, that we have world-class springtimes and as many trees as psychiatrists.

But let us try to accept acceptance, shall we? We might like it.