I have some very nice cat-friendly studios available between $1700-$1800 south of 78th Street. Just an FYI though... Landlords are generally not open to a rent reduction if you offer to pay advance rent. Actually, they're not permitted to receive more than the standard 1st month + 1 month security on a rent stabilized unit. All the best to you :-)
Licensed Real Estate Salesperson
Apartment updates available at http://www.christinegordon.postlets.com
"Home is where the heart is."
$1800 would be difficult in the West Village but push comes to shove $2500 (studio) may do it. In the East Village, maybe as Ming Gu proposes.
Good luck again.
P.S. There are three Path stations stops in the Village: 9th. and 14th Streets for Central Village and Christopher for the West Village.
There are apartments available in your price range, keep in mind there are very few apartments available to rent overall therefore if you find an apartment you like you must act quickly.
I will be happy to assist you locate your new home.
AC Lawrence and Company
A&I Broadway Realty
(718) 916 - 2355