NEWBURGH, N.Y. - Sunday morning in this small Hudson Valley city, more than 1,000 parishioners, most from Mexico, pack Spanish-language Masses at St. Patrick's Catholic Church. Afterward, many families flock to El Azteca for its authentic tacos. If somebody needs a ride home, there are at least a dozen local taxi companies catering to newcomers born in the Mexican states of Puebla and Jalisco. New residents from Mexico have, in the past four years, opened dozens of businesses that have begun to reinvigorate the ailing downtown district; they are the region's fastest growing community. It's the same story elsewhere in...