THE ARDUOUS task of choosing a new slogan for the District of Columbia has been completed, and the winner is: "Celebrate the City -- Discover the World!" It was chosen from some 5,000 entries among which -- given the city's current trials and troubles -- the double-entendres and puns were understandably numerous.

The winner isn't exactly memorable; it could just as well have been, "Discover the City -- Celebrate the World!" without anyone's noticing the difference. But it does have the virtue of not promoting local curiosities of nature, the climate or the supposed moral superiority of the population. Moreover, it contains no flowery adjectives, and as an exhortation to be printed on license plates (where it will be abridged to "Celebrate and Discover") it's certainly preferable to such grim imperatives as New Hampshire's "Live Free or Die."

The winning entry was submitted by Richard M. McWalters, who works in the District but lives in Virginia and had the good sense not to try to slip something like "Washington -- No Commuter Taxes Ever!" past the judges. His slogan (which replaces "Washington Is a Capital City") comes just in time, according to the tourism officials who conducted the competition. "I think we definitely need the new image," said Dan Mobley of the Convention and Visitors Association. "The negative publicity that was heaped upon this city . . . has definitely hurt."

Whether a new slogan will be enough to revive the lagging tourist trade remains to be seen, though. If it doesn't do the job, we'd suggest a more direct message for local license plates, perhaps something on the order of: "Washington -- No Slogan, But First Night's Lodging Is Free."