eBay lets you set search parameters so you are within the driving distance of the 5 boroughs and LI, so give that a shot.
Craigslist lets you see if anyone is hard up right then and if you catch the ad quick, you make out like a bandit.
Local nickel ad papers have the cheaper cars in them. Paid subscription papers have the better grade of goods as a general rule although some papers have an El Cheapo bargain section in the classifieds.
Look for bulletin boards to see who has what for sale.
Check out the car lots. At least you can look cars over to get an idea if that car is something you might like even if you don't buy it from that particular lot.
Banks and credit unions have repos for sale. Call up to see where they have them at.
Any place you go, watch out for the For Sale signs. If a store's parking lot lets people park vehicles for sale, check those places out.
Thrift stores that accept donated vehicles sell them.
Look for car auctions open to the public.
Good luck!
Rick