You may be stuck paying the penalty. Unlike with some types of contracts, there is no rescission period available in NY for lease agreements. Short of paying the penalty, your options are really three fold. Find someone to take over the lease, assuming its assignable; sublet the apartment; or try to negotiate something mutually agreeable with the landlord/management company. Given the length of the lease, aside from outright paying the penalty, the last option is likely your only practical alternative.
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The lease does not address this point?
In New York, a lease is not required to address the issue of an early cancellation, unless the tenant negotiated for the inclusion of that provision. Your lease likely provides that before signing the lease you had inspected the apartment, that all was good, and whatever the landlord promised to fix, is included in the lease. The purpose of that provision is that you inspect the apartment before signing the lease.
New York law considers that the entire rent for the whole three month period is due to the landlord on the first day, but by convention, landlords and tenants agree to split the entire rent into equal monthly installments.
Regardless of the actual lease provision regarding an assignment of the lease, NY law allows an assignment subject to the landlord's consent. An unreasonable refusal to agree to the assignment allows the tenant the option to cancel the lease on a one month notice. By the time you go through the time and expense of hiring an attorney and discovery of a potential assignee, your three month lease would be over.
So your choices are: Endure the lease and apartment for the three months you already owe, negotiate a buyout of the lease, negotiate and or pay the "penalty."
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.
While the other posters might be right, if you have the guts for it, and have paid no money, just do not do the lease. However, you are going to need a reason you do not like it which creates an issue of habitability to create a defense. For three months you are unlikely to be sued. If you are, you can settle it then.