As a police detective kept a watchful eye, President Barack Obama appeared to loosen his tie in the back of the presidential limousine as he sped away from the Gramercy Park Hotel last Friday night. Obama was in town to attend Al Sharpton’s National Action Network conference in Midtown on Friday afternoon, and later made a surprise dinner stop with his wife, Michelle, at Maialino, Danny Meyer’s trattoria in the E. 21st St. hotel. Arriving around 5:30, the couple and friends stayed until after 8, when POTUS and the first lady dashed off to attend Broadway’s “A Raisin in the Sun,” starring Denzel Washington.