Here are a variety of interesting resources, both primary and secondary, to get you thinking about possible areas of research.
Public use tabulations of visitors to areas administered by the National Park Service
1940s, attendance numbers
Newspapers, like ProQuest Historical Newspapers, will be helpful.
Large public libraries may have digitized collections of local interest; Chicago Public Library and San Francisco Public Library are two examples. Chicago PL even has a theater section of playbills from 1848-1922.
The taxi-dance hall : a sociological study in commercialized recreation and city life
Ebook version of a 1932 study.
Communications Act of 1934 (link to legislative history with all the related documents)
ProQuest Historical Newspapers may have reviews of popular radio programs
Radio's America : the Great Depression and the rise of modern mass culture
Making radio : early radio production and the rise of modern sound culture
Radio's civic ambition : American broadcasting and democracy in the 1930s
The listener's voice : early radio and the American public