Dear Floral Park Tenant:
New York landlords have tenants over a barrel when it comes to escaping the legal obligations of a lease even when the landlord breached the lease and failed to make repairs. All of that just provides a valid defense in a post vacating lawsuit if the landlord sues the tenant for the rent due to the landlord for the balance of the lease.
Instead, in NYC tenants are allowed the right to bring the landlord to the Housing Court and before a judge when the landlord fails to maintain the house or apartment and the landlord allows defective conditions to exist.
That is the HP Proceeding. A tenant starts off as you already did with notice to the landlord but you may follow up with a telephone complaint to 311 and then the lawsuit in Housing Court. You and you with a lawyer may very well use the HP Proceeding to settle the lease issues and allow for you and your family to move out without breaking the lease.
Read about the HP Proceeding at:
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.