The first BIG suburban May Company in Cleveland's eastern suburbs was "May's on the Heights" at Cedar and Warrensville Center Road in University Heights. Built before the advent of "Malls", the complex of three buildings was enormous. The rear "tower" was a nine story furniture warehouse. The restaurant wing featured a sawtooth roof and walls of glass. Then there was the store itself, originally designed to have five shopping levels, three of which were accessible to the acres of parking. It even boasted an auditorium on it lower level. The store was so large that the top floor was never opened. May Company avoided most 1960s and 1970s mall projects in the region. By the 1960s, the area was the heart of Cleveland's Jewish community and a major shopping destination.
Opened with great fanfare, Its decline began in the late 1970s when the tres chic Beachwood Place Mall opened further east on Cedar Road. Mays on the Heights died as a dinosauer in the 1990s when it torn down by its parent company for a multi-level urban mall.