Internet Archive
Digital Library, freely available. Includes many directories.
Library of Congress
Print, microfilm and digital telephone and city directories
FamilySearch
A Wiki with links to a range of United States city directories
HathiTrust Digital Library
A wide-ranging searchable repository
Ancestry Library Edition (on-site access only)
City directories and telephone directories
Fold3 (available at selected library locations)
City directories for many cities
*You might also consider contacting the relevant state and city libraries and historical societies.
Further research on the history of telephone and city directories at NYPL:
A Look at "The Book"
The Fall and Rise of the Telephone Directory
Direct Me NYC 1786
A History of City Directories in the United States and New York City
How to Research a Family Business
New York Public Library research guide.