Not particularly close to Logan, but the strip of Harvard Street in Brookline between Coolidge Corner (Beacon Street) and Comm. Ave in Allston, sometimes known as JFK Crossing, is one of the few Kosher centers in metro Boston (and it’s only about 2 blocks).
If you get there, I’d suggest Kupel’s Bake & Bagel for bagels, and the Butcherie across the street for appetizing (it’s more of a Kosher supermarket than a deli and can be quite a scene). http://www.butcherie.com/Buthcerie/SpecialN.htm
IMHO Kupel’s bagels hold up to any in New England (and I used to live within walking distance of H&H in Manhattan).
There are other Kosher shops scattered around the suburbs, Canton, Newton and Needham come to mind, but Brookline is the last place I can think of with any concentration.
There is an Anna’s Taqueria in the neighborhood, too. Popular, clean, cheap and good place for "Mission Style" burritos.
BTW – Rubin’s Deli, a block or so toward Allston is a sit-down Kosher deli. I’ve been told by Jewish friends that it’s the only Kosher deli left in Boston. But it’s pretty tired and does not get very good reviews for being anything but Kosher. For dining, you might do better toward Coolidge Corner for deli or nicer stuff, or in Allston for a crazy mix of ethnicities set in college grunge.