Not sure what part of Westchester you're in, but if you want to convert an old road frame here's a tip....
Check out the Salvation Army in Mount Vernon. Not sure of the exact address but it is near the Bronx/ Mount Vernon border. They usually have tons of old bikes.

Also you might want to check out the Metro Bicycles in New Rochelle... I'm usually not a fan of Metro but the guys that work at this particular location are pretty cool. Good luck!