There are various synonyms for the term "rundown section of city." Some common alternatives include "slum," "ghetto," "depressed area," "blighted neighborhood," "seedy district," "dilapidated zone," and "decaying locality." Other phrases that can be used instead of "rundown section of city" include "run-down part of town," "disadvantaged urban area," and "low-income community". These phrases typically refer to urban areas that are characterized by poverty, crime, and dilapidation. Synonyms are useful to avoid repetitive language and to provide variety in writing. However, it's important to use these terms with sensitivity and to consider the implications they may carry.