President-elect Donald J. Trump won the White House with an outsider’s populist promise to “drain the swamp” of Washington.

Now, as he prepares to assume the presidency, an open question remains about the capital he repeatedly spurned: Just how much is he willing to become a part of it?

Mr. Trump, a homebody who often flew several hours late at night during the campaign so he could wake up in his own bed in Trump Tower, is talking with his advisers about how many nights a week he will spend in the White House. He has told them he would like to do what he is used to, which is spending time in New York when he can.