Westchester County is beautiful. It's rich. It's got tons of golf courses for him and lots of accomplished, professional and politically connected women like her.

But of all the qualities that recommend this place as the new home of first lady Hillary Rodham Clinton and her husband, surely this has not escaped their attention: Westchester has picked every winner in statewide elections for 20 years.

As Westchester goes, so goes New York. "It's the weather vane county," says David Alpert, chairman of the county Democratic Party.

As she "explores" a bid to represent New York in the U.S. Senate, Clinton has focused her house search on this affluent suburban area north of New York City, home to Fortune 500 companies, commuting executives and professionals, soccer moms and a sprinkling of movie stars. It also has a robust political tradition that has produced the last three Republican governors. But in recent years, a majority of its residents have been Democrats.

The Clintons have decided they want to live in Westchester, the White House says, though how they will afford it and whether they'll rent or buy apparently have yet to be fully ironed out. Clinton herself said in mid-July that "if I could afford it, I'd buy." But with their multimillion-dollar legal bills from the various probes that have targeted them, it's not clear just how. Yesterday the first lady viewed a home in a surprisingly less posh part of Westchester than expected, though she and her husband haven't closed a deal there or elsewhere.

"They have several options they're looking at, and they're actively pursuing them," says Marsha Berry, Hillary Clinton's spokeswoman.

"There are no decisions that have been made," says Kathy Sloane, a broker from Manhattan-based Brown Harris Stevens who has known the Clintons for several years and is advising them in their house search. Clinton, for her Senate bid, has to become a New York resident by next year's election day. But she has said she is eager to find a place soon--perhaps to dispel the "carpetbagger" label thrown at her by those who resent her non-New Yorker status.

But like much else surrounding Clinton's possible Senate bid and her life after she leaves the White House, the house hunt is a secretive affair. So any sightings of Clinton in the region produce outbursts of speculation and bubblets of news such as the one that's gripped the tiny hamlet of Edgemont, in the town of Greenburgh, over the past few days.

Clinton viewed a $1.7 million house on 2.5 acres there--which sounds pretty splendid until you consider the thing that has Edgemont tongues a-wagging: that the house makes no sense for a woman of Clinton's ilk because, though it can't be seen from the street, its driveway empties onto a busy thoroughfare, Ardsley Road.

"It is a traffic jam," says a bewildered observer who did not want to be identified. "Everybody that knows Edgemont is saying, 'I can't believe there!' "

Edgemont is the most expensive section of Greenburgh (population about 80,000) but it's got none of the multimillion-dollar cachet of neighboring Scarsdale or North Salem, which at various stages have been ground zero for the Hillary House Hubbub.

Clinton reportedly liked those far northern portions of the county, home to such celebs as David Letterman, Christopher Reeve, Glenn Close and Mariah Carey.

Clinton herself has friends in Westchester County, including former White House counsel Bernard Nussbaum, who is working on Clinton's exploratory campaign's fund-raising. Rep. Nita Lowey (D-N.Y.), who wanted to run for the Senate but stepped aside when Clinton made her intentions known, also hails from Westchester.

That Clinton has chosen Westchester makes sense, of course, to Susan Tolchin. She's the spokeswoman for Westchester County Executive Andrew J. Spano, and she giggles and says things like: "Where else would you live after you lived in the White House? There's no place else."

Disputing the notion that it is a bedroom community for Manhattan, Tolchin proclaims, "We are our own entity." What she means is Westchester is "home to more Fortune 500 companies than any of the surrounding counties," and many of their executives live there.

It's a diverse place, she says. "You have people making $4 million a year and you have people who are making $40,000 a year. . . . Westchester is a microcosm of the state of New York." There are lots of minority executives and professionals among its moneyed classes, plus a sizable enough working-class population to lower the socioeconomic demographics that would otherwise be off the charts. There are no housing projects as such in Westchester, but there is some scattered-site public housing. The median house price is a surprisingly low $325,000, Tolchin says. The median annual income is $61,000.

Asked if Westchester is Clinton's choice because it's representative of New York, Berry says, "Ultimately, it's like all of our homes: We have to feel comfortable there."

And so does the Secret Service. Agents reportedly are checking out the houses as closely as Clinton herself, seeking a property with a spacious buffer for security.

"Their search is in many ways like the search of any homeowner," Sloane says of the Clintons, adding that it also is "in many ways unique because of the security requirements they have that really makes finding a residence a challenging task."

CAPTION: Mrs. Clinton viewed this 12-room house on 2.5 acres in Greenburgh, N.Y., this week. Price tag: $1.7 million.

CAPTION: Clinton has friends in Westchester--a majority of its voters are Democrats.