Central AC

If you have the unit inside the apt., it's going to be quite noisy.

Is it a trick question?

http://streeteasy.com/nyc/talk/discussion/19876-central-air-conditioning-in-a-gut-renovation

Might it work in a closet? I'd far rather that than ugly window units and the building we're considering does not allow any sort of venting...

The heat removed from the air has to go somewhere.

With window or through-wall AC, the heat vents outside.

If the whole building has central AC, then cold water is pumped to each apartment's AC units. The cold water absorbs the heat, the central system re-chills the water and exhausts the heat, and the cold water is pumped back. In winter it's hot water that loops through the system. Fancier buildings have four-pipe systems that allow any unit to either heat or chill throughout the year.

With your own central AC, refrigerant loops between an outside-exposed unit where heat is released and the air-handling unit where the refrigerant absorbs heat from the air.

In all these cases, cooling the air also removes moisture. In through-wall and window units, the water is spritzed outdoors. In a building-wide system, the moisture is drained away to the cellar. With your own central AC, the water is drained from the air-handling unit either outside or down a drain.

So yes, your central AC has to vent out.