Tenants with a valid lease are entitled to quiet enjoyment of the property, whether their tenancies are rent regulated or "free market." If a neighbor's activities are a continual source of agitating amounts of noise for excessive periods of time, the landlord has an obligation to remedy the problem. You should make your complaint in writing, specifying the nature of the disturbance, times of occurrence, and duration. These situations become somewhat more complicated when you are renting in a co-op or condo. For example, in a rental unit the lease may require you to carpet 80% of the floor area. But let's say the neighbor above you has hardwood floors and no such lease provision. In that instance, your landlord may not be able to do anything about children running back and forth all day and creating a commotion. In this or any situation involving ongoing, unreasonable levels of noise, you can ask the landlord to reduce the rent due to the diminished value of the premises. You'll probably have to retain a Tenants' lawyer and sue to get that abatement. If you go to Housing Court, you'll be on the blacklist even if you win, so it may be better to move. Your attorney can help negotiate an early termination of the lease, which is sometimes the best option.
A landlord is supposed to provide secure locks to your apartment when you move in. That means changing the locks from the previous rental, and giving you a new set of keys. If the landlord fails to change the locks and your apartment is burglarized, you can sue for damages. You'll have to prove it caused the theft and establish the value of the stolen property. The problem is that if you sue, and your lease is unregulated, the landlord is not likely to renew it. You may be able to defend against eviction by claiming the non-renewal is retaliation for asserting your rights, but then you will be involved in two lawsuits. Depending on the language in your lease and how a judge rules, you may not get reimbursement of your legal fees. A better solution is to ask the landlord if you can add your own locks, and supply the building's management with a set of keys, if they require it.
If you intend to sublet your apartment in New York City and you are the prime tenant, which means the rent is paid in your name, there's a multitude of important factors to consider. To ignore even one of them is to ask for trouble. The most critical point to keep in mind on any sublet transaction, whether your apartment is rent-regulated or a free market unit, is that you remain liable for most actions of the subtenants. This is the case even when you have the landlord's permission to sublet. That being said, two problems occur frequently: