Murphy's Law holds that the people you most want to impress always drop in when you look your worst, the house is a mess and the kids are fighting.

The law that says "If something can go wrong, it will" rings true for Salt Lake Mayor Palmer DePaulis this week.More than 170 mayors from 39 states will be in town this weekend, at the same time the City Council is fighting over DePaulis' proposed budget, the Salt Lake Police Association is picketing City Hall and Utah is executing its most infamous child slayer. (ee related stories on A1, B1.)

So, how does the weather forecast look?

Meanwhile, as DePaulis prepares for the 56th annual U.S. Conference of Mayors meeting in his city, he wants to tack just one word onto the

slogan that his most notable predecessor, city founder Brigham Young, made famous.

"This is the place," DePaulis will tell more than 170 of his national colleagues, "again."

That's what the banners lining Second South and West Temple boldly proclaim. And that's why city crews have been painting and sprucing up downtown, even down to setting out a fresh, unscuffed batch of the city's new garbage cans.

"We've painted everything that doesn't move. We've swept all the streets. We've even refinished the street benches," said Joe Anderson, city public works director.

"Salt Lake City is looking awfully good. They're really shining the place up," agrees Chamber of Commerce Executive Director Fred Ball. "I wish we could have the Conference of Mayors every year. I am most delighted that they've turned the fountain at Symphony Hall on."

DePaulis, himself an eternal optimist, will concede that Salt Lake City bashers have been especially vocal as of late. And having the nation's urban bosses in town for a June weekend is a timely opportunity to do a little image polishing.

Hosting big-time mayors like New York City's Ed Koch, Marion Barry of Washington, D.C., and Detroit's Coleman Young is enough to swing national attention out West. But having Democratic presidential hopeful Michael Dukakis come wooing urban support just one month before his party's nominating convention adds to the prestige of the conference - and the amount of national press it is expected to receive.

Among the more than 700 mayors, staff members and press representatives expected for the conference will be a goodwill mission of 10 Taiwanese mayors, led by Mayor Hsu Shui-teh of Taipei City.

Nationally, Utah often suffers image fallout when bizarre, fanatical crimes - such as the Mark Hofmann bombings and the Singer-Swapp shoot-out - hit national headlines.

No help to the state's tourism peddlers are words like "prudish" that are brandished by non-natives.

In a February article written by Los Angeles Times writer David Lamb, Salt Lake City was depicted as a Perry Como kind of place.

"An America of the '50s holding out against the beat of heavy metal," Lamb wrote about Salt Lake City, describing it as a place where residents consume record-breaking amounts of bubble gum and Cracker Jack and are deprived of opportunities to attend an X-rated theater or see discarded beer cans on the streets.

That's why conference planners have gone out of their way to impress visiting mayors with cultural events that not only show how unique the city is - that's where the Mormon Tabernacle Choir fits in - but also how normal it is. "This is definitely an image thing," DePaulis said.

"We're going to have the Mormon Tabernacle Choir. Where else can you hear the Tabernacle Choir?" said Emilie Charles, DePaulis' administrative assistant.

A special issue of Utah's own Wasatch Ale beer, imprinted with the "This is the place - Again" logo, will go into a free bag of gifts every conference-goer will receive.

Pioneer heritage is fine, but when national cameras are focused on Utah's capital city, local conference planners want to show off more than just the covered wagons that got the city's founding fathers here 141 years ago. When the mayor talks about impressions he would like to create, he uses words like sophisticated, progressive and refreshing.

Sunday evening, the mayors and other visitors will be treated to a downtown street party on Second South, highlighted by the finest cultural performances the city has to offer - Ballet West, the Repertory Dance Theatre and Utah Opera. Another evening, mayors will be whisked to Snowbird's swanky Cliff Lodge and will eat dinner in the shadow of Big Cottonwood Canyon's spectacular mountain scenery.

"We're going to show off that we do know how to lighten up," Charles said, referring to this week's advice from an imported team of urban planners, who said the city was too organized and stuffy.

Pat Holmes, convention services manager of the Salt Lake Convention and Visitors Bureau, says the state's 100,000 annual convention visitors spend an average of $477 in the state.