They have refused to correct the mistake. I have asked them about 3 times and finally given up and just cancelled my membership.
If you are going to sue, and can prove they overcharged - consider going to the small claims court. It should cost you $15 + time - unless you loose quite badly - in which case its conceivable the court could award costs against you (I don't know if this is true of the small claims court in NY).
You can represent yourself, so no heavy legal bills.
It will take a a few hours of your time to prepare and have the hearing.
Of-course, very often, just by filing you will get the opposing party to sort out the issue - and probably won't even need to go to court.
Can you sue? Yes. Will you win? If they are in violation of your contract, probably, if they might be in violation? still probably but there is a huge risk that you will have to pay court costs and lawyer costs. Is it worth your time, no.