Hi J.,
Welcome to NY! I'm originally from Wisconsin (Oshkosh) and moved to the NYC area 10 years ago. I have lived in New Rochelle the entire time -- as some people have mentioned, there are pockets in all the larger cities of Westchester (Yonkers, New Rochelle, Mount Vernon, White Plains) that you wouldn't want to live in. However, all of these cities have very beautiful areas as well (I live in a very lovely neighborhood on the East Side of New Rochelle at the Larchmont border). But if you are looking for a small-town feel with excellent schools, I highly recommend Eastchester, Tuckahoe, Scarsdale, Pelham, Larchmont, Harrison, and Rye. These are all in the southern part of Westchester County. The catch is that these are affluent areas and rents are high --also, it's rare to see a 4 bdrm apt/house for rent in areas like Eastchester and Pelham. You'll probably have more luck in areas like New Rochelle, White Plains, etc should be able to find a 4 bedroom apartment in a multifamily home. Unfortunately, rents around here even for a 2 bedroom usually start around $1600-- 4 bedrooms will be at least $2000 and go up to $3000 and more (in good neighborhoods).
I suggest you call a realtor based in Westchester and enlist their services. Their fees are usually equal to 1 month's rent but it is totally worth it if you are unfamiliar with the area. I can recommend one person - she's a mom our age (mid 30s) who grew up in Westchester -- I don't know if she handles rentals per se, but if not she could point you in the right direction. Her name is Robyn and here is a link for her contact info: http://prucent.com/robyn_rosenberg
Good luck and if you need more info or help just email me!
-L.