In the dark days after the 1980 election, when he and other officials of Jimmy Carter's administration were mulling over what to do with the rest of their lives, Stuart E. Eizenstat received some unexpected advice from his father. On a visit here, Leo Eizenstat told his son, the assistant to the president for domestic policy, not to come home to Atlanta.

"He said, 'I'd rather have you happy 500 miles away than less than happy next door,' " Eizenstat said. He grinned, recalling the sage counsel of his father, who died in February.

"I think he knew me better than I knew myself," he said.

What the father knew about the son is that Eizenstat is passionate about the development and execution of public policy. He thinks about it, thrives on it, is happiest when he is elbow-deep in memoranda. So while Carter returned to Plains, Eizenstat was one of the Georgians who remained at the center of government and public policy-making, becoming a Democratic presence in Ronald Reagan's Washington.

In the almost six years since, that presence has grown considerably, flourishing in a city that has been dominated by conservative Republicans. Eizenstat, 43, heads the Washington office of Powell, Goldstein, Frazer and Murphy, the Atlanta law firm he worked for before joining the Carter presidential campaign and going to the White House.

From a deliberately modest beginning of two lawyers during the Carter years -- "I didn't want anyone thinking we were peddling influence," said senior partner Elliott Goldstein -- the firm's Washington office has grown under Eizenstat to 27 lawyers, with clients that include Westinghouse, IBM and International Paper.

In the long and ongoing legislative battle over tax revision, Eizenstat was among lawyer/lobbyists retained by a coalition of high-technology firms and universities seeking to retain tax credits for research and development. The tax credit is in both the Senate- and House-passed versions of the legislation.

A trial lawyer by training and inclination, Eizenstat is today mostly a lobbyist, representing clients in the halls of Congress and before the regulatory agencies. But he would never be confused with an inhabitant of "Gucci Gulch," the stereotypical high-priced, high-powered Washington lobbyist.

Eizenstat has a wry sense of humor, but above all he is seen as a serious man who views public life and public issues seriously -- and who is to be taken seriously. At the White House, his personal stature grew even as Carter's political fortunes were tumbling. That trend has continued.

David Rubenstein, his deputy at the White House and now a lawyer with another firm here, calls Eizenstat "the best lobbyist to hire in this city" because of his knowledge of government and the "incredibly diligent" attitude he brings to his work.

"Members of Congress like him for two reasons," Rubenstein said. "He returned their phone calls when he was in power, which is something they don't forget. And he has intellectual underpinnings to what he's doing. He believes in what he is doing."

Bruce Holbein, manager of government relations for Digital Equipment Corp. of Boston, which Eizenstat has represented, strongly urged the coalition of high-tech firms to retain Eizenstat in the tax-revision fight. His reasons, Holbein said, went beyond the question of "access," that vaunted Washington commodity that Eizenstat enjoys with Republicans as well as Democrats on Capitol Hill.

"You've got to have both an outstanding public-policy position and the ability to do effective lobbying on a day-to-day basis," Holbein said. "There are very few lobbyists in Washington who bring both of those skills together. Stu, if not unique, is among a handful."

Eizenstat said questions of public policy are "what has really animated my life since college." At age 24, he was on the White House research and speechwriting staff of President Lyndon B. Johnson. In the 1968 presidential campaign, he was research director for Hubert H. Humphrey, whom Eizenstat still calls "my hero."

After the Carter presidency, Eizenstat passed up far more lucrative offers from larger law firms to take over the fledgling Washington office of Powell, Goldstein. The firm, in turn, made a major commitment to finance the expansion. Goldstein, remarking that Eizenstat "has always been able to do most anything," said, "Stuart said, 'This is what it is going to take,' and we had enough faith and confidence in him to make the investment."

In his lobbying, Eizenstat said, he tries to draw on his experience as a trial lawyer and senior White House official. One rule is "always go to the staff first," because eventually the member of Congress will check with the staff.

And like a good trial lawyer, Eizenstat said, "you damn well better be prepared to understand the other side's argument."

Despite the rapid expansion of the Washington office, the lobbying-legal business is only one of at least three major preoccupations in Eizenstat's professional life. Another is the Democratic Party, about which he has written extensively and many of whose public officials consult him regularly on a broad range of issues.

In 1984, New York Gov. Mario M. Cuomo called Eizenstat and read him portions of an early draft of his keynote address to the Democratic National Convention. More recently, Eizenstat has reviewed speeches for former Virginia governor Charles S. Robb and written a "domestic policy/political strategy" memo for Sen. Joseph R. Biden Jr. (D-Del.), a likely 1988 presidential contender.

The third of Eizenstat's "worlds," as his friends call them, concerns Jewish affairs. Eizenstat, who travels frequently to Israel, is a member of several Jewish organizations and is completing four years as chairman of the advisory committee of the Institute for American Jewish-Israeli Relations of the American Jewish Committee.

Earlier this year, Eizenstat was, as usual, deeply involved in several of these pursuits. Although he flew once a week to Boston, where for the last four years he has taught a course on presidential decision-making at Harvard University's Kennedy School of Government, he also headed a task force to determine the impact of the Gramm-Rudman-Hollings budget law on Montgomery County. A county resident, he said he took on the latter task in part from a sense of civic duty and because he is an unabashed public-policy junkie.

"I like that sort of thing," he said.

Meanwhile, Eizenstat also was organizing a "unity symposium" that brought together leading rabbis from American Judaism's three often-feuding branches.

All this has served to enhance Eizenstat's reputation since he left the White House. Kenneth R. Feinberg, a lawyer and former aide to Sen. Edward M. Kennedy (D-Mass.), put Eizenstat "in the vanguard" of his generation of Washington lawyers who will eventually replace such eminences as Clark B. Clifford and Lloyd H. Cutler.

"It seems to me you have a few lawyers in town who will be looked on not only to solve a problem on the Hill, but as a sort of brain trust, valued for their judgment," Feinberg said. "One of those who comes first to mind to fill those shoes is Stuart Eizenstat."

There is also the possibility of a Democratic administration in the future and a return to government service for Eizenstat. He said he does not seek that, observing that he is happy where he is and that "I've seen a lot of people hurt personally in the process of putting together an administration."

Naturally self-effacing, he added: "How many positions would I be interested in?"

Still, there is the lure of the public-policy arena, which Eizenstat has long found irresistable. "It's a lot more fun to be making it than to be recommending to others how they should make it," he said.

His friend and former deputy, Rubenstein, put it this way: "Stuart wants to be a player."