inner-city area; city center
Refers to the central part of a city, often used in contexts like real estate, commuting, or describing urban facilities.
Apartments in the city center have high rent.
I want to live somewhere with convenient access to the inner-city area.
中心部 means 'central part' and can refer to any center (city, organization, etc.), whereas 都心部 specifically means the urban core of a city.
Compound of 都心 (としん, 'city center') and 部 (ぶ, 'part' or 'section').