Of course I have to put in a plug for my own institution:

Marissa C. Weaver
Executive Director
America's Black Holocaust Museum
2233 N. 4th Street
Milwaukee, WI  53212
(414) 264-2500

Also note, the last time I checked there were over 180 black museums that were
members of the African American Association of Museums -- as another respnder
mentioned, this would be the best place to start your search.