One of the places that came to my mind when thinking about this was the Lower East Side Tenement Museum. Located on 97 Orchard Street in New York City's Lower East Side, the museum is a tenement that was built in 1863 and tells the stories of the nearly 7000 working class immigrants who lived there.
There's no cutting edge technology or expensive exhibits. You might expect that the building would have been renovated to show what it looked like in 1863 but they have endeavored to keep it preserved in the state that it was purchased in 1988. Only small sections of the tenement have been restored in an effort to intimately illustrate the lives of the families who inhabited the apartment at various points in the building's history. Each apartment tells a different story and each visit is a different and unique experience. The museum is only viewed by guided one hour tours and there are several different tours to choose from in which you will learn about an Italian, Irish, German or Jewish immigrant family. On each tour you will be walked through the tenement by a tour guide who will reconstruct the lives and struggles of the families who started new lives in America.
Walking through the cramped and stuffy apartments was a very moving experience. By being immersed in the space you are really able to get a feel for the hardships endured by the immigrants.
Museums are no longer just buildings designed by famous architects with priceless art on the walls. Traditional museums have evolved and perhaps the definition of the word "museum" needs to be modified. I think the Tenement Museum has redefined the role of museums. Its not just a building with old stuff in it but an educational, historical and cultural experience that was deeply touching. I loved the Lower East Side Tenement Museum and would definitely go back to take another tour.