"We all want a place that fulfills all our dreams. And it's my job to keep Beverly a place where dreams can be fulfilled. It is a continuing struggle to maintain the quality of life." -- Mayor Donna Ellman, Beverly Hills, Calif.

"The quality of life? For crying out loud, we're just trying to survive." -- Mayor Thomas H. Cooke Jr. East Orange, N.J.

It was the annual midwinter conference of the U.S. Conference of Mayors, two days of meetings and workshops at the L'Enfant Plaza Hotel, where the participants discussed everything from "Public/Private Partnerships" in the Degas Salon to "Tax Policy and Leasing" in the Monet Room. This year the big subjects were the New Federalism and the prospect of more budget cuts, and yesterday the conference president expressed the prevailing opinion. "The president's State of the Union address on Tuesday night did not include the current state of the cities," said Mayor Helen Boosalis of Lincoln, Neb., at a press conference. Reagan's long-term approach to problem-solving, she said, "failed to address the problems that mayors must face today."

Still, the problems vary, and they don't conjugate the urban verb the same way in Beverly Hills as they do in East Orange. The question of what is important finds different answers depending on whether the constituents are worrying about losing a job or finding a good gardener. Yet, the notion that a community celebrated for its affluence is somehow without problems is one that annoys the mayor of Beverly Hills.

"Despite its great social image, Beverly is really a microcosm of the rest of the country," says Donna Ellman, 56, of her town of 32,000 nesting on 5 1/2 square miles in the middle of Los Angeles. "We're just trying to maintain ourselves as a low-profile, small-town residential area in the heart of a big metropolis. There's such a great deal of pressure from the outside world wanting to move in. I like to think of Beverly as an anachronistic Camelot surrounded by a world of Clockwork Orange. We're trying to maintain a heavenly, idyllic place in a world that is constantly trying to impinge on it."

It is not that Ellman is oblivious to the differences between Beverly Hills and the real world. With a $40 million operating budget and an investment portfolio which yields between $9 million and $10 million, Ellman likes to describe the city's financial situation as one of "transient solvency," pointing out that $10 million is hardly going to buy Beverly Hills the new police and fire stations it needs. Still, Ellman recognizes that solvency is a word most mayors would have to look up in a dictionary these days.

"We are different from other cities," she says. While other cities are actively seeking foreign investments and banks and that sort of thing, "we try to selectively accept." Banks, for instance, often try to come into the city, according to Ellman, but often there's "no sense of loyalty, no appreciation of us as a community. All they want is the address."

One begins to understand. Forget the mansions, the Mercedes Benzes, the swimming pools, forget for that matter, Rodeo Drive and the Rolls-Royces double-parked in front of stores that will take your money by appointment only -- Beverly Hills is not just another pretty place.

Ellman, whose brisk efficiency and easy smile collide with the image of languid luxury so often associated with Beverly Hills, likes her town best on Sundays, when the stores are closed and the tourists are gone "and the streets are quiet and the Little League games are going and the parents are walking their kids in strollers. It's little America, it really is." Other Side of the Tracks

East Orange, N.J.: Population, 90,000. Twelve miles from New York City, next door to Newark, a bedroom community with a budget that is currently about $3 million over the amount the state legislature says it can legally spend. Mayor Thomas Cooke, a former high school teacher with close-cropped graying hair and an air of grim determination, figures that this year East Orange has lost over half a million in revenue-sharing funds, about the same in block grants, and over a million in CETA funds. Meanwhile it picked up about 1,500 more welfare recipients after they were dropped from the federal rolls, and the unemployment continues to rise. "Problems?" says the mayor of East Orange. "Yeah, you could say we've got some problems."

The cost of school lunches had to go up. So did the cost of public transportation. More than 200 city workers will have to be laid off. For the first time, the layoffs may have to include public safety employes. The emergency fund for residents too poor to pay for heat and hot water is nearly gone, and it isn't even February.

Young couples are losing their first homes, unable to meet the payments. The real property taxes on which the city depends for its revenues have already been stretched to the limit. "How much can you tax people?" asks the mayor of East Orange. "For crying out loud," he says. He says that a lot. Little America's Problems

There are also problems in little America. Commercial rents in the city are sky high and while it's no problem finding a fur-trimmed anything in Beverly Hills, Ellman says it's getting increasingly difficult to find a decent dry cleaner or cobbler, or any of the other mundane businesses that can't pay the kinds of rents that stores which cater to gilded fantasies can afford.

But although there are, without question, what Ellman calls "the Gucci-ites" inhabiting Beverly Hills, the idle rich who "run from beauty shop to beauty shop and massage to massage," there are also celebrities who care.

People like Monty Hall, for instance -- "whenever you need him, he's there" -- and Doris Day -- "she used to live up the street and she was an absolute collector of stray dogs, you always knew where to look if one was lost" -- and Debbie Reynolds -- "she was a Girl Scout leader, and no matter what she was doing, she was always back for her meetings." The spirit of volunteerism is not dead, says Ellman. "I would guess that more money is raised out of Beverly Hills than anywhere else in the country. We're really pushovers for charitable causes." The New Federalism

The mayor of East Orange says he has tried to make ends meet. In his first term, he went after the delinquent taxes owed by the big businesses in town by threatening foreclosure. He tried to cut down on the number of public employes. He says he has even tried to take the president's advice on volunteerism and the private sector. He tried to get volunteers for an auxiliary police force but only 12 people offered to help. He doesn't blame those who didn't volunteer. Most of them, he says, are looking for paying jobs. What about contributions from the business community? The mayor just laughs. "You're kidding."

Cooke is not pleased with the solution that the Reagan administration has proposed for his problems. "I'm very warm, you're perfectly right. This whole thing on federalism is based on the idea that the states will deliver to the cities. Let me tell you about states' legislatures. For crying out loud, what makes them think that the urban areas are going to get a fair shake from the rural areas and the sprawling suburban areas that dominate the legislatures?"

"You just get fed up to here," he says, the anger simmering in his voice. "We're the people on the firing line. Whatever the effect is, whether it's a cutback or an elimination of a service, it's not the president who did it, it's the mayor who did it. The mayor," says Thomas Cooke. "Me."

"You tell me where the justice is," says the mayor. "People think welfare is the biggest rip-off, but they're not the ones who are against farm subsidies or subsidies for corporations. They complain about a measly $3,000 per pupil education cost, and then they're willing to spend $10,000 to $20,000 keeping a person incarcerated. Tell me where the justice is in that."

It is not, the mayor says, that he is insensitive to what the president is trying to do. "We're all sympathetic to the need to cut back government spending and cut through the government regulations that effect service delivery. But it is inhuman to tell the people to freeze to death now and starve to death now and that it will all be justified in 1991."

Ellman, though, a Democrat like Cooke, thinks the president's plan is "interesting as long as it's phased in properly." She thinks cities will have to get increased taxing authority to go along with the increased responsibility for social services.

The mayor of Beverly Hills will soon be passing these troubles on to someone else. Her term ends in April, and she has decided not to run for the City Council again. It is time now, she says, to devote herself to more personal goals. Ellman has lived in Beverly Hills for the last 25 years, having come to California from Chicago. "I always dreamed of living there," she said. "It was something to aspire to, like something in a Horatio Alger story. If there weren't a Beverly Hills, we would have to invent one."

Last fall, the mayor of East Orange won a second term. He is asked about the future. "What do I think is going to happen?" says Thomas Cooke, sitting ramrod-straight in his black, three-piece suit and staring ahead. "I've given a lot of thought to that." He looks down for a moment, then looks up. "What with the number of people who want to work and who can't work, and the escalating crime wave," he says, "the only thing I foresee is insurrection in the streets."