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Peekskill has some houses that might fit the bill, at the lower end of that market, but parts of the area are not very nice, and the house might need work. However, if you're willing to look in Connecticut, you can find a small house or a townhouse around that price point in Danbury.
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All the world's a stage, and all the men and women merely players: they have their exits and their entrances; and one man in his time plays many parts, his acts being seven ages.
~William Shakespeare (As You Like It Act II, Scene VII)