Whether a closet is connected to the Floo Network depends on whether it has magical fluctuations. As for where it specifically connects, only its owner and the Ministry of Magic know.
This manor was originally given by Sirius to the Order of the Phoenix to be used as a contact point.
We can guess that since Sirius was the owner, this closet might lead to the home of his good friend Lupin—well, Lupin didn't have a home.
Chapter 130