New Yorkers are to get their first look this week at something Baltimore and Boston residents have been enjoying for years: a fancy waterfront mall built by the Rouse Co. of Columbia, Md.

South Street Seaport Marketplace, a sprawling collection of restaurants, shops, cobblestones, classic architecture and many of the other features that have made Harborplace and Faneuil Hall huge successes, is to open the first of its renovated doors on Thursday.

The first 40 stores and eating places will be ready for the opening of the $351 million lower Manhattan project, which will eventually comprise nearly 200 establishments and 250,000 square feet of selling space.

The reconstructed buildings and a newly built pier jutting into the East River tie into the South Street Seaport Museum, a flotilla of old ships and accumulated seafaring memorabilia that is already a major tourist attraction.

The opening of the Seaport will cement Rouse's place as the premier builder of urban malls, particularly those, like the Baltimore, Boston and New York projects, located in once-rundown waterfront areas. The Rouse imprint is also on waterfront projects in Norfolk and Toledo created by Enterprise Development Co., a separate company run by Rouse Co. founder and chairman James Rouse. (See Story Page 21.)

But building stylized waterfront malls is not all that Rouse does. The company is one of the nation's largest owners and operators of shopping malls, with nearly 60 dotted around the country. It is also involved in real estate financing and developed Columbia, Md., the 60,000-resident planned community located between Washington and Baltimore where Rouse is headquartered. Rouse Co. has more than $1 billion in assets and earned $8.1 million last year on revenues of $163.6 million.

"Things for the Rouse Co. are terrific," says its president, Mathias J. DeVito.

But business has not always been so good. A decade ago, Rouse was foundering in red ink--a victim of the bursting real estate bubble during the late 1960s and some ill-timed diversification moves into apartment and office building construction.

"The reason they got into trouble was they took their eye off the ball," says Robert Frank, who follows the company for Alex. Brown & Sons, the Baltimore brokerage house.

DeVito says that as a result of the lessons of the early '70s, the company is managing its real estate interests more conservatively.

Among other things, the company is no longer "banking" land--accumulating property with an eye toward future development. The company now generally buys land only for specific projects. "Having gotten caught with land in 1972 and 1973 and 1974, we've made it a policy that we're not going to do that again," DeVito explained.

The company has also decided to stay away from the short-term financing common to much real estate development. "That kind of gobbled up the cash flow of other projects," DeVito says. Since 1980, Rouse has financed all new projects with long-term loans, in some cases using newly available sources of money such as pension funds, which become partners in projects rather than just lenders.

And by purchasing older centers and renovating them, the company avoids the three- to six-year time lag involved in building a mall from scratch.

When an acquired mall has been less than successful before Rouse took over, the company has been able to stoke sales by giving the malls the Rouse treatment--applying many of the design and marketing techniques that have made Harborplace and Faneuil Hall so successful. Sales at Staten Island Mall, a large New York shopping center acquired by Rouse three years ago, are up 75 percent since the mall was renovated.

Rouse's business plan calls for constructing two new malls a year, acquiring two existing centers and expanding one of its older centers.

Now under way is the giant 1 million-square-foot Painters Mill Mall in Owings Mills, north of Baltimore, scheduled to open in the mid-1980s.

"Their focus is clearly their expertise in downtown renovation," says Frank. In addition to the well-known waterfront projects, Rouse is also working on downtown shopping centers, such as its Grand Avenue project in Milwaukee and Gallery at Market East in Philadelphia.

In Washington, Rouse is building the retail section of National Place, the block bounded by 13th, 14th, E and F streets NW, which includes the National Press Building and a new Marriott hotel. The center is to open in fall 1984 with several levels of shops and eating places.

Last week, Rouse began renovating Union Station in St. Louis into a collection of shops and restaurants. The company is also looking at projects in Chicago, New Orleans, Miami and several other cities.

"They're a legitimate part of what I consider a renaissance of the central city," DeVito says of the downtown centers. "This is a different kettle of fish than a Harborplace.

"You've got to be asking yourself when you're building these things: Why are people going to come here?" he says. "If you can provide an experience there that is beyond what is available in the suburbs, that's another reason to go."

South Street Seaport, which when completed will be larger than either Harborplace or Faneuil Hall, shares with those projects the restoration of a blighted area of urban waterfront. Located in the shadow of the Brooklyn Bridge, a stonecrab's throw from the Fulton Fish Market--part of which is incorporated into the project--Seaport is an easy noontime stroll from Wall Street.

Rouse is not financing the entire Seaport project. Following a pattern it has used elsewhere, the company is protecting itself by sharing the job with the city, state and federal governments and private investors; Rouse's investment is $90 million, about 25 percent of the total cost.

Like Harborplace and Faneuil Hall, Seaport will be a collection of small shops and restaurants, their offerings attuned to the surroundings--from prints of sea scenes to New York egg creams. The establishments are located in a group of restored buildings as well as new structures that echo the surrounding architecture.

It's a formula, with some variation, that has served Rouse well in Baltimore and Boston. "You're really trying to create a marketplace that really is an important part of the city," DeVito says. "It can't be a carnival. . . . It's got to be a real, legitimate piece of urban development that has integrity."

Not everybody is enamored of Rouse projects. Plans to renovate Chicago's huge Navy Pier as a Harborplace-type development have been criticized by some politicians and businessmen in the city who worry about the planned center's effect on downtown traffic and retailers.

The Navy Pier project is currently in limbo as a result of the recent change in administrations in Chicago. Navy Pier was a pet project of former Mayor Jane Byrne, but DeVito says Rouse has been encouraged in its early contacts with Byrne's successor, Harold Washington.

There have also been problems in Boston, where several Faneuil Hall merchants recently filed suit against Rouse, charging that they have been overcharged for taxes and other expenses. Rouse officials deny the charges.

And in New York, there has been grumbling from fishmongers at Fulton Fish Market, who complain that even though attempts have been made to integrate the fish market into the project, development at South Street is squeezing them out of the area they've occupied for more than 150 years.

There has also been skepticism about parking availability in the area, although Rouse officials say the parking situation at the Seaport is not much worse than it is at Harborplace or Faneuil Hall.

But those complaints are not expected to hurt the South Street project. Rouse officials note that the Seaport Museum is already drawing 1 million persons annually, and the neighboring Wall Street area provides another 500,000 potential customers daily.

"I really don't have any doubt about the potential of a place like South Street Seaport because of the market there," DeVito says. "I really don't believe that New Yorkers will be able to go anywhere in that city and do as much as they can do in that spot."