HOUSE OF ‘VAIN’

CARLY Simon is making it no secret that selling her West Village co-op is the right thing to do.

The legendary pop star is listing her two-bedroom, two-bathroom duplex in a Federal-period townhouse on Commerce Street for $3.8 million.

And she believes that nobody will sell it better than her sister, Joanna Simon, an accomplished opera singer and, perhaps more important, a broker/vice president at Fox Residential Group.

“Carly has used her unique style and taste to create a romantic and intimate home,” says a source familiar with her 1,200-square-foot pad on a tree-lined block. “She’s selling mainly because she lives nearly full-time in Martha’s Vineyard these days.”

Simon gut-renovated the apartment in the intimate three-unit building after she bought it four years ago.

The purchase came after a well-publicized dust-up between her and the co-op board at the Dakota, where her application to buy a one-bedroom apartment for $999,000 was turned down – reportedly over her desire to add an extra bathroom.

Simon’s West Village digs were featured last year in InStyle and will be offered with or without her tasteful furnishings.

Perry big hurry

Heather Mills can’t wait to get settled into her new West Village apartment.

In a follow-up to our breaking story last Saturday, sources tell us that the ex-wife of Sir Paul McCartney has moved the closing date up to July from August for her two-bedroom apartment in the glassy Richard Meier building at 173 Perry St.

We also hear that she’s paying just under the $5 million asking price for the ninth-floor digs, which will include most of the Meier-designed furnishings.

Mills might have asked for an earlier closing so she’ll be free to dash out to the Hamptons in August, which was her modus operandi last year when she rented the East Hampton home of Nick Pileggi and Nora Ephron.

Brown Harris Stevens listing broker Hilary Rovins had no comment.

Beach bummo!

Rachael Ray might be able to cook a meal in 30 minutes, but it’s taken her considerably longer to come up with the scratch to buy a vacation house.

Nearly a year after we first reported that she was buying a Southampton mini-compound (and over six months since she went to contract), the cooking-show host/donut queen and her husband, John Cusimano, have finally closed on the property that had a $2.9 million asking price.

Included in the 6.2-acre spread is a three-bedroom, three-bath European villa-style main house. There is also a two-bedroom guest cottage with a kitchen and a sauna, plus a separate one-bedroom cottage. The property, located by the Southampton Golf Club, has a pool, a pond and multiple gardens.

Prior to the contract signing, the golf club and the property’s owner were at odds over the exact placement of the property line. After both retained legal counsel, an agreement was finally reached last December for an undisclosed settlement.

According to Ray’s spokesman, Charlie Dougiello, the property encroachment issue caused a delay in Ray and Cusimano’s mortgage process.

“It worked out better because they ended up getting a better rate,” Dougiello says.

Listing broker Tim Haftel of Prudential Douglas Elliman could not be reached for comment.

Couch-surf turf

Rudy Giuliani has a new place to crash in case things don’t work out with wife Judi.

According to city records, Howard Koeppel and Mark Hsiao, the gay couple who put up the then-mayor when he split from wife number two, Donna Hanover, in 2001, have paid $2.37 million for a high-floor apartment at 100 Riverside Blvd. The three-bedroom condo in the Avery development includes river views.

Koeppel, a Queens car dealer, had been quoted as saying that Giuliani was clean, “always made his bed” and “called me mother.”

The bottom line

When we mentioned a few weeks ago that Ted Koppel had lowered the price of his Washington, DC-area house by more than half, we thought maybe he’d finally unload it.

Now comes word that the former “Nightline” host has lowered it . . . again!

We have followed the property’s financial slide since Koppel first put the nearly 9,000-square-foot home in Potomac, Md., on the market in 2005 for $4.1 million. Last August, the six-bedroom Contemporary with an indoor pool was lowered to $2.3 million. As of earlier this month, Koppel was asking $1.94 million.

But now, some savvy buyer can have it for $1.79 million. Washington Fine Properties has the listing.