The Greek Festival in Arlington is the 2nd, 3rd, and 4th of June. For a little more information http://www.saintathanasius.org/
(there will be chowish food -- spit roasted lamb, 2000 lbs of Souvlaki, and they are also looking for volunteers)
That Saturday and Sunday are the first of the summer feasts and processions in the North End (I don't have details, but saw a bulletin with this). Sunday is the 60th anniversary of La Festa della Repubblica Italiana at Christopher Columbus Park.
June 10-12th is the Irish Cultural Festival in Canton. http://www.irishculture.org/festival/ (More of a music and culture oriented event, but there is chow and guinness)
For Portugese June 10 - 11, 2006 - Festa de Santo António, centered out of the Igrega Santo Antonio, in East Cambridge at the corner of Cambridge and Card. Medeiros.
Also Portugese National Day is coming up on June 10th, but and the Portuguese Counsel has a whole series of events (some of which have already started), although chowish ones seem to be relegated to various local restaurants and a couple of "gala" dinners.
http://consuladoportugalboston.org/bp... (if its portugese, there is a link for an English version).
More on Brazilian "festas juninas" and hopefully more detail on these later on.