There are 4 main exhibition i could mention after visiting Museum of the City of New York, which also may inretesting for you:
“Ain’t Nothing Like the Real Thing: How the Apollo Theater Shaped American Entertainment”, which traces the evolution of the Apollo—from its origins as a segregated burlesque hall to its starring role at the epicenter of African American entertainment and American popular culture. The Apollo Theater in NYC is one of the most famous music halls in the US, and the most famous club associated almost exclusively with Blackperformers. It is listed on the National Register of Historic Places . Nearly all forms of entertainment—comedy, dance, swing, jazz, rock ‘n’ roll, soul, hip hop, and more—were welcomed on the Apollo stage. Serving as a place where African American performers could start and advance their careers, the Apollo helped to launch the careers of some of the best-known names in entertainment—dancers Charles “Cholly” Atkins, Sammy Davis, Jr., and Bill “Bojangles” Robinson; band leaders Cab Calloway and Duke Ellington; comedians Redd Foxx and Jackie “Moms” Mabley; and musicians ranging from Louis Armstrong, James Brown, and Lionel Hampton to Billie Holiday, Aretha Franklin, and the Jackson Five.
Timescapes(on the second floor in museum), an engrossing 22-minute multimedia experience, traces the growth of New York City from a settlement of a few hundred Europeans, Africans, and Native Americans to its present status as one of the world’s great cities. The film features animated maps and archival photographs, prints, and paintings from the Museum’s collections. I advice everybody who is going to visit this museum to watch this movie. It doesn t matter how much you know about the City, 
because this clear movie will structure everything you knew before, make it more accurate and moreover give you new knowledge.
Very interesting to see there New York interior for 1690-1906. Extraordinary furniture and different decorative objects made in New York from the colonial era to the dawn of the 20th century. Really when you see the old elements of interior (despite that it was just a hundred years ago) you understand how great progress in comfort and design we have now.
And the last exhibition that i could mention is “On the move: Transportation Toys from the Permanent Collection”. On the Move is a special installation of toy and miniature vehicles from the Museum’s Permanent Collection that not only suggest the lives of the children who played with them but also reveal how transportation evolved and changed in the 19th and early 20th centuries.