At one point you're going to want to have a buyer broker assist you anyway so you may as well find one now (see link below) and then put them to work.
I can even set it up to search just for a specific elementary school, since Scarsdale has 5 if you have your heart set on just one specific one.
Westchester is unique in the fact that we have P.O. box addresses which is not the same in the rest of the country so the common search engines like Trulia, Zillow and Realtor.com are not always set up accurately which can be frustrating.
Also, having been in the area for so many years, I will be happy to also guide you on what is a busy street or far from the train, if you are not local and have questions that need to be answered about specific listings.
Prudentinal Centennial Realty
We're looking for more agents & offer commission splits up to 80% with no fees.
Keller Williams Realty
The best way to run a search is to have a local real estate agent run the search on the MLS using your specific search parameters. The MLS system allows for specific school district searches, even down to a specific elementary school.
I would be happy to run a search for you.