The Hills of Scottsdale, Ariz., face the great dilemma: choosing to make a move to better their careers or better their family life.Grant Hill’s interest in joining the Knicks and being slotted as their starting shooting guard on a potential Eastern Conference contender is growing by the day, and there is a sense he is leaning toward the Big Apple.The Bulls and Clippers have been mentioned as possible landing spots for Hill, who has played the past three seasons with the Suns.KNICKS 2011-12 SCHEDULEHill would be playing in the New York spotlight, where a basketball renaissance has taken place. He would be thrust into the basketball mecca and his wife, Tamia, a recording artist, would be in the media and musical mecca. She is expected to release a new album in two months.Tamia Hill played a Central Park concert last summer. Her profile would rise even more in New York with her basketball-star husband starting for the Knicks and her having a permanent spot on celebrity row in the refurbished Garden.“Every time they visit New York and then leave, they always say, ‘Boy, we should get a place here,’’’ one person familiar with Hill’s thinking told The Post. “They love New York.’’The Suns may be a disaster this season, as they go through a rebuilding phase, reportedly deciding to waive Vince Carter when the lockout officially ends. But as crucial are Hill’s two daughters, who are in elementary school in Scottsdale — fourth grade and kindergarten.The person familiar with Hill’s thinking said he never has been willing to live away from his children and he would likely bring them along for the Big Apple ride.But as another Hill confidant said, “Scottsdale is hard to give up.’’ Hill has showed up routinely at the Suns’ practice facility to work out since Thursday, when teams opened their buildings for voluntary workouts as the lockout draws to an official close.Hill’s teammate, Jared Dudley, gave both sides of his conundrum. “He doesn’t have any choice but to come back,’’ Dudley told the Arizona Republic. “We need him here, we’re already thin as it is. “His family’s here and we’ve got his training staff for him. At the same time, he’s at a point in his career where everybody wants to win.’’With the former Duke Blue Devil aboard, the Knicks’ starting lineup would be Chauncey Billups, Hill, Carmelo Anthony, Amare Stoudemire and Jared Jeffries, who agreed to terms yesterday. It’s full of veteran savvy and leadership. Hill could be the missing leadership ingredient and ensure Stoudemire and Anthony never put their own needs above the team. Knicks brass also was concerned guard Landry Fields may not be ready for a starting role.Hill played for Mike D’Antoni in his first season in Phoenix in 2007-08, but Hill already has rejected the Knicks two years ago to sign a two-year deal with the Suns.“Exceptional character in the locker room,’’ one Phoenix source said. “It’s very hard to find anyone better than Grant in a locker room.’’It is why Steve Nash said over the weekend “it was very important’’ for the Suns to keep him. Suns general manager Lon Babby, Hill’s former agent, called Hill his highest priority. Hill still is represented by Babby’s D.C. law firm.Last month, Hill attended the Garden to watch Duke coach Mike Krzyzewski set the Division I record for victories. Hill crossed paths with Knicks executive Allan Houston. Soon they may be crossing paths a lot more.