MANCHESTER, N.H. — This city has long been a resettlement site for refugees, sent here by the State Department for a chance at a better life. More than 60 languages are spoken in the school system, with Somalis, Sudanese, Iraqis and other recent arrivals mixing with children whose ancestors came from Quebec to work in the mighty textile mills along the Merrimack River. But this year, after decades of taking in refugees, Manchester said, “Enough.” In a highly unusual move, Mayor Ted Gatsas and the city’s Board of Aldermen asked the State Department in July to halt resettlements here for...