Rather than recreate the wheel, there are a number of threads on the Forum where the issue of operating a business from your home in NYC is discussed. The threads focus more on the practical than the legal aspects.
viewtopic.php?t=10723
viewtopic.php?f=3&t=10739
viewtopic.php?f=3&t=10836
There are undoubtedly more thread that touch on this, but these popped up quickly. You can search the Forum for more, looking at words such as business, working, clients and so on.