They absolutely do not have the right to enter the apartment without
reasonable notice (see below). Thank you for letting us know about
this -- I _am_ vacated and am now weirded out by the idea of brokers
coming in to my apartment while I'm away.
http://www.oag.state.ny.us/realestate/habitability.html
Tenants have the right to privacy within their apartments. A landlord,
however, may enter a tenant's apartment with reasonable prior notice,
and at a reasonable time: (a) to provide necessary or agreed upon
repairs or services; or (b) in accordance with the lease; or (c) to
show the apartment to prospective purchasers or tenants. In
emergencies, such as fires, the landlord may enter the apartment
without the tenant's consent. A landlord may not abuse this limited
right of entry or use it to harass a tenant. A landlord may not
interfere with the installation of cable television facilities.
(Public Service Law §228) .