There used to be some cat 5 hotels out in Queens. But I think with devaluation they are now all cat 6 and higher. Not sure if there are any now near the city.

This is actually a nice hotel for a cat5:
Stamford Marriott Hotel & Spa
243 Tresser Boulevard Stamford, Connecticut 06901

It is a few blocks to a train station but will take about an hour to make it to Grand Central on the local train, Metro North. Trains run fairly often.

There is a nice mall and plenty of restaurants all within walking distance. Does get slippery if snowing in October.