The big event, you'll know it by the name even if you've never been to it before or ever heard of it at all is A Taste of Mystic. I don't really grasp the use of the indefinite article since there isn't another taste of Mystic to my knowledge but since I'm someone who doesn't know what he doesn't know, I may not be a very good person to ask.
Less well-known but lots closer to my house, one is a three minute walk and the other is maybe ten minutes away (tops) are a pair of festivals that share more than just a Mediterranean heritage. The 35th Annual Grecian Food Festival (they let people with grey hair in, as I would know) started yesterday and finishes up on Sunday at the Holy Trinity Greek Orthodox Church on Washington Street, about half a block from NFA.
At the water's edge, technically in Howard Brown Park, for one day only tomorrow, it's The Taste of Italy. My family makes it a point to get there every year and judging from the turnout, at both events, so do more and more other people. Here's a write up from one of our local papers on the two festivals, and you can be forgiven for drooling on the mouse pad as you read the menus.
Soon enough the weather will cool and the days will grow short as we start to bundle up against another New England winter-but we ain't there yet, so pass the baklava and pizzelles and don't talk with your mouth full.