Ossining has many nice areas; generally the ones that are down by Sing Sing or in that general area are the rough ones. And anyway, you don't want to live in a house where your lights dim once a week (that's a very old joke, Lord forgive me...)

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Drive southbound on route 9 and use that as a dividing line. The areas to your left are generally better than the ones to the right. There are areas out by route 9A that are gorgeous.
This being said I dig all of Ossining. It has great character. I went to a barbecue one night at a friend's house who lived across from the prison gate. We heard them calling the guys in from the yard over the loud speaker.
There are great cafes, restaurants, places to hang out, a great library and a metro north stop to get you into Manhattan. And don't forget to visit the Ossining Museum.
I can't help with the school system, I don't know much about except that its got diversity which is good for kids.
