These days, most of the NYC dance club scene is house music. Funk music is almost impossible to find, and hiphop clubs are rare.
Some clubs are more for the dancers, some more for the music. Each club has a different vibe, energy, and etiquette (cyphers? do people vibe out? crowded or spacious? lot of people drinking or not? good place for finding that special guy or girl? etc) There is a small summary below, but the best way to get a feel is to just go and see for yourself.
You'll find a lot of parties on http://www.dancedeets.com/?location=NYC, be sure to check the same week as many things are last-minute.
FOR PROMOTERS: Please be aware that this is for visitors who may only be in town for a week, looking to make the best use of their time because they just spent thousands of dollars on a trip to come to NYC. If you want your party on here for dancers, please try to promote to your usual dance communities first...as that community is what the dance tourists are looking for anyway. :)