At the present moment, there is 1 single family home on the market that meets your criteria priced at $510,222 in Briarcliff Manor. This particular property is close to the Pleasantville Metro North station (about 1.5 miles). It takes about 45-51 minutes to travel to Grand Central during morning rush hour.
Here is the link to the Pleasantville station:
Please find another map with stations surrounding Briarcliff Manor. Stations on the Hudson and the Harlem line including Ossining, Scarborough that are near Briarcliff Manor. Just click on the station for further information.
As for schools, you need to do the research yourself. You can check out the following link:
Keller Williams Realty Group