New York City - 3* or 4* Hotels Near Airports in NYC

We have been looking for hotels in the NYC Manhattan area for almost 2 weeks. We booked one night (Sunday 10/24) at the Westin Times Square for $120. We haven't been able to find anything within our price range for Monday and Tuesday nights. We are needing 6 rooms. We are now looking for hotels that are out a ways from the city ~ hoping to find lower rates. We will leave NYC Wednesday morning at 9:30am from JFK. What I need to know is what areas would have nice hotels at cheaper rates with good transportation to Manhattan areas and JFK Airport, as we will not have our own transportation. Any help identifying areas would be greatly appreciated!

You might want to try the Sheraton LaGuardia in Flushing, Queens. Yes, it's obviously more convenient for LGA but JFK is a straight shot down Van Wyck Expressway (though it can be congested at certain times of the day).

It's pretty convenient to the Main Street, Flushing terminus of the #7 line which goes to Times Square.

It's in the middle of a block with a bunch of Chinese shops, food stores and restaurants so if you really like Chinese food you're in luck (that part of Flushing is heavily Asian).