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Yorktown, Somers, Cortlandt in Northern Westchester are all great options. Mahopac in Putnam county will add another 10 mins or so to your commute, but you will find more newer homes there in your price range. Good luck!
If it's not too late for you, check out Briarcliff Manor. There are some nice condos that could be in your price range. We love the school and the community.