Been looking for this for a while... All I can remember is that it takes place in current day; aliens carve out a scoop of Manhattan (I think) for their huge spaceship's zoo. The humans break out and start exploring the other 'cages'. Each cage has a different habitat -- I think some have different gravity.
I also think this same author (pretty sure it's a man) wrote another novel about present-day alien invasions, also dealing with gravity.
Any help would be appreciated!