Mayor Cory A. Booker has a high schooler’s affinity for Twitter, reveling in its ceaseless flow of affirmation and infinite space for self-promotion. But the occasional perils of his reliance on the social media service became evident on Wednesday when a 26-year-old stripper from Oregon revealed her private online correspondence with him. In a message to the stripper, named Lynsie Lee, Mr. Booker wrote that “the East Coast loves you, and by the East Coast, I mean me.”