I can partly answer your question.
You mentioned New Orleans. Its population declined very much after Hurricane Katrina in (2005?) flooding, which destroyed many houses and left many residents homeless, but it has steadily increased somewhat again.
Washington D.C. population was majority Black during the 1970s - 1980s - 1990s after the violent race riots in 1968 and the increase in drug-related murders and homicides. The homicide rate stayed high through the early 1990s, and then it fell and declined (decreased) steadily. Many young, educated, professional, white people have moved into the city because they feel safer now, and moved into neighborhoods that were Black before. They are also many new apartment buildings. At the same time, large numbers of younger and middle-aged Black people moved from Washington city into the eastern suburbs (Prince Georges County) beginning in the 1970s.
The word for this is "gentrification"
http://en.wikipedia.org/wiki/Gentrification
New York City has also improved in the 21st century. The subway cars in the 1970s-1980s used to all have ugly, graffiti writing on them, but now they are kept behind a fence where vandals cannot paint on them. Times Square used to be full of pornography and prostitutes, but now it's been cleaned-up. White people have been moving into the famous Black "Harlem" district which used to be a scary place people were afraid of. (Ex-President Bill Clinton I think, has an office in Harlem). The parts of Brooklyn that are closest to the Brooklyn Bridge are now very popular with young white people, also Hoboken New Jersey. New York City also has a quite low crime rate now.
Many Black people have moved from
Atlanta city into the suburbs. Suburban DeKalb County (including Decatur) to the east, now has a majority Black population, and there are also many Blacks in the south suburbs near the Airport.