OP, it isn't necessarily by neighborhood, since planning units aren't the same thing as neighborhoods. Most that I know of contain at least two planning units, and sometimes may feed to different elementary schools. The true Westover area feeds to McKinley but around the margins to the west and north are units that feed to Tuckahoe and/or Nottingham.
There is map on the Arlington website that you can blow up. Alternatively I think you can type in a particular address and it will list the planning unit. Layer in the Planning Area and zoom in and it will show you planning units and tell you the schools they are zoned for..
http://gis.arlingtonva.us/gallery/map.html?webmap=efd4da094f7841d0bff522d037697bd9
This map shows where the boundaries will be starting in 2015 down to the street level.
http://www.apsva.us/cms/lib2/VA01000586/Centricity/Domain/110/Supt%20Recommendation%20-%20Variation%20B_Street%20Map.pdf