We're in the Abingdon ES district as well, but like many of our neighbors have done, we plan to send our son to Claremont, which is one of Arlington's two bilingual immersion elementary schools (Key is the other). You have to fill out a transfer application, but according to the 2011-2012 Arlington Public Schools Handbook, "Abingdon, Hoffman-Boston and Oakridge have guaranteed admission to Claremont before its defined feeder schools: Ashlawn, Barcroft, Carlin Springs, McKinley, Nottingham, Randolph and Tuckahoe." So none of our neighbors in the Abingdon school district have had problems getting into Claremont.
See the full handbook here (pdf):
http://www.apsva.us/cms/lib2/VA01000586/Centricity/Domain/8/APSHandbook2011-12.pdf
And a quick search for "Claremont" in this forum will show you that it's becoming a popular option with parents in Arlington.