Charlie Sheen left a trail of doughnut crumbs, clam shells and ink stains during his madcap exit from New York in the wee hours of yesterday morning. The self-proclaimed warlock began his run with a farewell dinner at City Island Lobster House Monday night, sources said, where he and his posse dined on baked clams, shrimp cocktail, pasta and steaks. Then they headed north, stopping along the way for dessert at a Dunkin’ Donuts. That was followed by a 4:30 a.m. appointment at famed Big Joe & Sons Tattooing in White Plains, where Sheen goddess Natalie “Natty” Kenly was inked with a compass on her right forearm. In tribute to Kenly’s West Coast roots, the compass only had a “W” and no “N,” “S” or “E,” store owner Adam Kaplan told The Post’s Andy Campbell. Sheen and tat-meister Joe Campagna also went over a secret design for a new tattoo that the “winning” actor will supposedly get in a few weeks. Sheen and Kenly also paid a visit to the store’s back room to take pictures of Campagna’s 4-foot- long corn snake, Lilly.