the house is accessible from the New York city center via xxxx road, xxxx road and finally onto an unnamed road which leads to the property. The New York city center is about 1 mile away from the house.
It is fine to use "the." In this case. More natural would be:
The house is accessible from the central district of New York ...
... The center of New York is about 1 mile away from the house.
That is a puzzling sentence, because the center of New York could be interpreted as having a size of greater than one mile in diameter.If it is one mile from the center, it probably