English/Spanish. Connie’s Mexico Café is Wichita’s oldest family-run Mexican restaurant. In 1963, Concepción and Rafael López opened Connie’s Cafe. They were both born in Mexico, Rafael in the state of Nuevo León and Concepción in Jalisco. They grew up during a tumultuous period of in Mexican Mexican history. North of the border, the U.S. economy was booming and labor was in demand. Some U.S. industries, particularly railroads needed employees and actively recruited Mexican immigrants. Well over half settled in the state’s urban areas, including Wichita, where they worked for either the railroads or the meat packing industry.