Each of the links below provides access to organizations that offer at least some free resources.
ArchiveGrid – local archives and repositories in the United States
This article is from 2013 and some of the links might be outdated, but it’s still a fabulous starting point:
250+ Killer Digital Libraries and Archives
State Genealogical Societies:
Historical and Genealogical Societies of the U.S.
Ethnic societies :
Federation of Genealogical Societies – has many ethnic societies, but database is in ABC order so you will have to scroll.
Major Genealogy Collections in Libraries: