A good portion of the homes in the "PO" that are located near the Village border were in fact built by the Lawrence family, who were the major developers of the Village. It was designed to look very much like the Village and it does to this day. Lawrence Park West, Armour Villa and the Cedar Knolls Historic District are very similar to Bronxville proper, and in many cases are within walking distance of Village ameneities.
In terms of Coop apartments it is much the same. There are beautiful prewar buidlngs with wonderful apartments on Midland Avenue, Bronxville Rd, Parkview Avenue and Pondfied Road West. They are available for far less cost than the Village, and the Boards are far more reasonable.
While I cannot discuss specifics about schools as it is prohibited by Federal Law, I can tell you that my Coop has many young professional families with children and I do not hear complaints. Taxes are definately far lower than Bronxville, and the small income tax surcharge does not make up the difference.
I have lived in the Bonxville PO for almost 20 years and I have found it to be a safe convenient place to be. My suggestion is to have an experienced Realtor show you the area and its strenghs, and at that point you can make an informed decision if it is for you.