hey - i'm in nyc too - but at the actual public pools (the rec center pools). 2 people plus you in a lane in a city of 12 million is not so bad. a lot more space than you get on the subway.
the main thing is to nod or acknowledge the other swimmers when you or they get in the lane. this action will increase your odds of being forgiven in that deeply patient way that real ny-ers frequently demonstrate (often without the tourists noticing). don't introduce yourself - just say hi or nod when they get to your end of the lane - gesture for them to go ahead, and when they get far enough in front of you to be now danger of you passing go ahead and start swimming.
something i've found is that sometimes there is a "fast" lane and someone starts doing slow breastroke in between laps of freestyle. try to avoid this -just do some warm up strokes in one lane, switch to the faster lane for faster strokes, and switch back to the slower lane for drills or cool downs.
most important - if you take a break and stand around, stand in the corner of the lane furthest to your right (if you are facing back up the lane) so you don't block people or confuse them as they try to turn.