Looking for 1 bedroom in a shared/separate home.

Hi, I'm looking for a bedroom in a shared or separate apartment or home by April or May in the areas surrounding NYC but not in the city as I prefer the suburbs and parking. I work from home as a social worker. I am organized and responsible and can provide references if needed. My budget is ideally up to $1500 for my own apartment or 1300 for a shared space.
I have a well-behaved quiet cat that can stay in my room for most of the time. I can provide references of past happy landlords. :)