Do you mean neighborhoods like Harlem in NYC?

Uptown in North Chicago and Chatham/Grand-Crossing in South Chicago have become home to one of the biggest African immigrant populations in the United States. This partly violates /r/askhistorians rule on recent history, so I'll try to tie in some historical context to broaden this explanation.

Chicago has seen its African immigrant population more than quadruple since 1990. Ethiopean, Ghanaian, and Nigerian immigrants represent a large share, but Eritrean, Senegalese, and others have fair representation in kind. Chicago is and has been, for a long time, a "City of Neighborhoods" and the unique politics of neighborhoods have encouraged certain trends.

Uptown has played many roles in the past century; an upper-middle class white neighborhood, a favorite neighborhood to gangsters, a brief hotspot for Latino families, "hillbilly central" in the 60s and 70s as white transplants from the South came in, and more. Uptown's unique housing policies, which allow for a type of adult dormitory otherwise illegal elsewhere in Chicago as far as I am aware, made the neighborhood especially attractive to immigrants."Little Vietnam" firmly planted itself on the north end of Uptown, and since the 90s, Uptown has become a major site for new African immigrants coming to the city.

Conversely on the southside, we have Chatham/Grand-Crossing. It was historically a quite well off Jewish neighborhood well into the 1950s until a combination of social and political pressures saw conversion into more of a middle-class black neighborhood. While much of the rest of the southside around it grew increasingly violent throughout the 60s and 70s, Chatham/Grand-Crossing remained a paragon of middle class black American families. Following the boom of African immigration in the 90s forward, the area became a popular choice for African immigrants who had become more culturally and financially established in the city.

Neither area is explicitly called "Little Africa" or "Little Ethiopia" or what have you, but there's a reasonable chance that they could be in the future. Uptown especially. The conversion of the Argyle Street area to becoming known as "Little Vietnam" is a phenomenon that's only arisen since the 1970s. Provided another 20 years, the "Sheridan Park" sector of Uptown could very well become "Little Ethiopia" or "Little Nigeria".

My Twenties/Thirties maps of NYC show Spanish Harlem, Italian Harlem, and Negro Harlem uptown. My friend is an expert on the Chicago Black Belt during Prohibition.

Most large cities had black neighbrhoods. They later called them ghettoes. The residents all came from the same country - the US, usually from the South if traced back a while. Jim Crow America did not have much Caribbean or African immigration. And I have heard "Little Africa" used.

I can't speak for all cities, but there is a little Ethiopia in Los Angeles