If you are talking about החנות this could be "it is located in the city center," couldn't it?
"centre of the city" implies the geographical centre while "city centre" implies that it's where the city is most active, popular, etc.
More or less:
the city centre - מרכז העיר
the centre of the city - המרכז של העיר
I would disagree. In AE, "center of the city" can also mean where all the activity happens, essentially "לב העיר", whereas "city center" might be a specific location with that name.