I've lived in NYC for a while and even living in Inwood I have never seen rats in buildings I've lived in.... only on the track bed at subway stations (their "natural" environment) There was a time when I took a walk through Washington Square Park at night and saw one run out from the bushes.
Roaches though, they're everywhere. I saw one in the 4th floor bathroom at the Time Warner Center (where there's the super luxe Mandarin Oriental Hotel and multi million dollar apartments- how did they get in there??) to a few out for a night walk on the sidewalk in Bay Ridge to Forest Hills and even Riverdale... when I asked landlords while apartment hunting if the building had roaches I would usually get the response of "This is New York- every building has at least 1 roach"
Bed bugs though are worse than roaches
and rats though. From what I hear you defiantly don't want them and the only way to get rid of them for good is just short of having your building demolished since they can invade other apartments.
When I lived in the city I was super paranoid about getting them since they're making a resurgence and can live anywhere where people sit or sleep, even on subway cars now (thankfully only in the motorman's compartment as far as we know).