"大城市的中心区" can be translated into English as "the central area/district of a major city" or "the downtown area of a big city".
"Central area/district" emphasizes the geographical centrality within the large city.
"Downtown area" is a more colloquial term commonly used in American English to refer to the busy, central part of a city.
Both expressions are appropriate, depending on the context and the desired level of formality.