Prepositional phrase modifying multiple nouns
Although the five boroughs of NYC are now coextensive with separate counties, your sentence needs to separate boroughs and counties in some fashion. If your client is unhappy with as well as, you can write:
We have appeared for decades in the five boroughs of the City of New York and in Nassau, Suffolk, and Westchester counties.
Even though Nassau County and Westchester County would be capitalized when used alone, in the plural the word ceases to be a proper noun and is not.
The noun phrase five boroughs of the City of New York seems both too formal and redundant. There are no other entities called boroughs in New York, but if there has to be an additional modifier, five New York boroughs should be plenty.