From grime to shine. Missing out on massive urban renewal may be the best thing that ever happened to Providence, R.I.

TARNISHED by press clips that mention urban decline and underworld ties, this Eastern Seaboard city has had trouble attracting and keeping new business. But now this 350-year-old city is riding the wave of New England's resurgent economy and working hard to spruce itself up to lure business and investment.

City officials and community leaders, however, recognize that it's going to require a good deal more than cosmetic improvement. The city's reputation has done a lot to stunt its growth.

``Providence's image needs as much renewal as its economy if we are to compete with the region's big cities,'' Mayor Joseph Paolino Jr. says. Recent arson attacks on Union Station and the Outlet Company, two of the buildings targeted for renovation, cast additional doubt on whether substantial changes will be achieved in Rhode Island's capital city.

But ``cities can overcome stereotypes,'' says Richard Gureghian, director of communications with the Massachusetts Executive Office of Economic Affairs. Southeastern Massachusetts - just across the state line from Providence - is very vigorous now, Mr. Gureghian says, but it first had to overcome problems similar to those facing Providence today.

Mayor Paolino is confident his city can compete with its larger neighbors. He recently launched a $300,000 advertising campaign to promote these indications of revival:

The city is preparing for a huge $300 million retail, business, and hotel complex called Providence Place, which will fill the 30 acres of vacant land between the State House and downtown, known as the Capital Center.

The river's edge in downtown Providence will be the site of a $120 million project called the Foundry, with 200 specialty shops and a 300-room Sheraton hotel.

The city's two rivers are being moved back to their original banks to make the waterfront more visible and accessible.

A city convention center is scheduled to begin construction this fall.

Restoration of historic residential areas and plans for new housing are accelerating.

Billboards around the project area call Providence ``the city that works,'' for business, residents, commuters, and students. The ads speak of lower housing, business, and living costs, and the presence of prestigious colleges (Brown University is here) for those who are looking for a fast-growing, yet historic and small-scale, city.

When driving through Providence, however, one doesn't see the destruction usually associated with such large-scale urban renewal. No city blocks have been leveled to make room for progress.

Instead, narrow streets that stripe the sloping land overlooking the state capitol are lined with cobblestone sidewalks and rows of newly redone colorful old clapboard homes. Along the waterfront, once-deserted warehouses made of brick, sandstone, and wood now house restaurants, stores, apartments, or the developers who converted them.

Even shopping centers look as if they grew in this city where no building is higher than 30 stories, observes Joseph Cerilli, president of the Providence Land Company, which rehabilitates old structures here.

Why? The city was too broke to participate in the heydey of urban renewal, when ``they'd go into a city and knock down 10 blocks and start over,'' says Alexius Conroy, president of Conroy Company, one of the three developers working on the huge Providence Place project. So the city retained its small scale and many of its historic buildings.

Local preservationists, cooperating with developers, have worked hard to protect this historic fabric, ensuring that new design is blended with old-style architecture. This has brought about what many call the city's ``renaissance,'' says Ken Orenstein, director of the Providence Foundation.

``It may be the only thing Providence has over other cities,'' says Wendy Nicholas, executive director of the Providence Preservation Society. Adds Mayor Paolino: ``We work with our historic agencies so we can preserve rather than destroy.''

``Preservationists have prevented us from tearing down older buildings to make way for new,'' says Ronald Kutrieb of Capital Growth Companies and a former president of the Providence Foundation. But not much friction has been generated, because most developers don't want to change the city's historic look or its scale, Mr. Kutrieb adds.

The mayor attributes many of Providence's remaining problems to the fact that other New England cities aren't aware of these changes. He hopes - through his campaign - to alert businesses in the ``overcrowded'' and expanding markets of Boston, New York, and parts of Connecticut to what Providence has to offer.

``The basic structure of Providence is very sound now ... and it has a very healthy and positive political environment,'' says Mr. Conroy.

This is reflected in a 40 percent increase in housing prices over the last year, the largest gain in the United States, says Gary Ciminero, chief economist at Fleet Financial Group. Moreover, the number of jobs is growing so rapidly that there has been a large influx of out-of-state workers, Mr. Ciminero says.

This has contributed to Providence's falling unemployment rate, he says. As of March, the metropolitan area had a 4.2 percent unemployment rate, down from a high of 10.2 percent in 1982, according to United States Department of Labor statistics.

While some of the recruited out-of-town chief executive officers have responded with an ``are you crazy?'' attitude when Providence was mentioned, others are expressing an interest in the city. American Telephone & Telegraph Company has two offices in Providence, one of which just opened to take advantage of the good labor force, and an attractive, high-quality living and working environment, a company spokesman says.

The influx of businesses is helping to draw attention to changes taking place all over New England's smallest state, as well as fueling growth in its capital city.

``What this brings to downtown [Providence] is critical mass,'' says developer Conroy, adding that this mass is now ``large enough to encourage other things to happen.''