The Nets' goal is to make Brooklyn the new mecca of basketball in New York City. They have specifically targeted strategies in taking aim at the Knicks and have consistently made comments about their intent to steal the spotlight. Even the Nets players have talked about Brooklyn being a better team. Everyone's excited about playing in Brooklyn.
Just not living there. 

The Nets are still looking for a practice facility in Brooklyn, and as a result, will still be out in New Jersey. That's creating a split of where the players are living, and it turns out that none of them will actually be living in Brooklyn. 

From the New York Times: 

(Deron) Williams is renting in SoHo while shopping for a permanent home, preferably one with easy tunnel access. He will have company. Joe Johnson, the Nets’ newly acquired All-Star guard, forward Kris Humphries and guard Jerry Stackhousewill all be living in Manhattan as well.

Seven Nets will reside in New Jersey, including the rookie Tyshawn Taylor, who got an apartment in Hoboken, his hometown. (Two others, Mirza Teletovic and Tornike Shengelia, are playing overseas and have not yet shopped for homes, but they are likely to end up in New Jersey, too.)

via For Nets Players, Play in Brooklyn, Practice in New Jersey, Live In ... - NYTimes.com.

Williams, specifically, had trouble finding a four-bedroom place for his family in Brooklyn, but most of the players told the Times it was just a matter of logistics, getting between the games and the practice facility. If and when the Nets get a new facility in Brooklyn, most expect to move there, as it will be just as convenient. 

In reality, a huge number of NBA players never buy a place where their team is. Why spend the money when you're on the road for 41 games of the year and you can be traded at any moment? But there is a certain amount of smirk-worthy humor in the fact that the Nets players, whose franchise is touting the burough as the new center of all things basketball in N.Y. are all living in Manhattan, closer to Madison Square Garden.