I discovered the Ethnic Heritage Center (http://www.southernct.edu/ethnic_heritage_center/) courtesy of a recent discussion on H-Connecticut and am very impressed with what I've found. Based in new Haven, the Ethnic Heritage Center houses five ethnic heritage groups. Researchers interested in using the collections of The Greater New Haven African American Historical Society, The Connecticut Irish American Historical Society, The Italian American Historical Society of Connecticut, The Jewish Historical Society of Greater New Haven, and The Connecticut Ukrainian American Historical Society only have to make one stop. The Ethnic Heritage Center has a library designed to make access to these collections and the university's own ethnic resources simple.
The EHC is more than just a research library. It also houses exhibitions and events for each society. Their website is out of date on this subject, but listings should be available from the local news sites. These exhibits appear to be a way to get a feel for the site without knowing what you need to research.
If your family represents any of these ethnic groups, you may want to pay a visit to the EHC.