I've been to the City a good many times, never stayed at a hotel there though. My SO is from there, but she only replied, "New Jersey." And that's clearly not a good idea (sorry, Warbler). Looking at expedia, there are hotels in decent parts of Manhattan for as low as $150/night in October (granted the rooms look budgety). I could offer some idea about various neighborhoods if you are considering any particular ones.
You could always go upstate, pick apples and such ;)