General Synonyms:
* City center
* Central business district (CBD)
* Inner city
* Urban core
* Midtown (in some cities)
* The heart of the city
More Specific Synonyms:
* Main Street (if the city is known for its main street)
* The Loop (Chicago)
* The Financial District (New York City)
* The West End (London)
Informal Synonyms:
* The city
* The hub
* The center
The best choice will depend on the specific context and the desired level of formality.