Westchester Country Club used to be the home of the Barclays for the better part of four decades.  Then, after a falling out between the Club, its membership, and the PGA Tour, Westchester was out as host of the event for all but one year between now and 2012. 

The 2008 rendition of the tournament was played at the Good Doctor's Ridgewood CC in New Jersey to a lot of fanfare and critical praise.  The 2009 edition is already slated to play at Liberty National Golf Club.

Still, we don't have a 2010 site for the event.  That may change soon, according to Rex Hoggard at the Golf Channel.

Sources at Plainfield (N.J.) Country Club confirmed the club is in negotiations with the PGA Tour to bring The Barclays to the Donald Ross-designed layout in 2010.

Ty Votaw, the Tour’s executive vice president of communications and international affairs, would not commit on any ongoing negotiations nor would he give the timetable to announce the 2010 Barclays venue. Votaw did, however, confirm that the Tour’s plan is to create a rotation for the event in the greater New York City area.
 
“We want to make sure we move it around to some of the best courses in the area,” Votaw said.
 
Plainfield hosted the 1987 U.S. Women’s Open, which was won by Laura Davies, and the 1978 U.S. Amateur which was won by John Cook.

So, the lack of a home appears to be by design much in the same way that the Western Open BMW International is being moved around the midwest but always back to Chicago.