It's possible, but you will likely be looking at an apartment in a multi-family home at that price point. Many of the newer buildings run to higher rents, but I'd also suggest looking in parts of New Rochelle or the nicer parts of Mount Vernon, since there are some gated co-op communities that would be around that price in a rental. The co-op rentals may require board approvals, however.
If you don't mind the extra travel, you could find that price point in Peekskill without too much of a search, but all is not lost in Port Chester, though you might have to look around to find the right property. You could also check Connecticut, Stamford and Norwalk areas to stay on the Sound, but be a little further out.
Check on the Westchester-Putnam MLS website for information regarding current offerings. And, check Craigslist for the by owner rentals which might be your best bet for the multi-family poperties in Port Chester.
Here's a link to the WPMLS website:
MLS
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