The Aran Sweater Factory has a nice selection, and you should visit the aran islands, but the absolute best are at O'Maille. You could be talking 3x the price of the other hand knits, but they're stunning sweaters. The owners put a lot of effort into buying from the absolute best knitters, as well as helping ensure that younger knitters are trained (most are old women, if you visit the islands you'll see them sitting around chatting in shops and whatnot as they knit). When I was there this summer, the owner showed me a sweater knit by, in her words, one of the best knitters ever. The tiny little details on that thing were just stunning- the ribbing at the bottom had alternating designs of cable knit, a feature that was described to me as, "just showing off". And it was the thickest and densest sweater I have ever held. Encounter one of those things, and you'll never look at a 'heavy' sweater the same again.
They also did the wardrobes for The Quiet Man, back when that was filmed in the area, and have stuff like tweed jackets and other traditionally irish clothing. Certainly worth a stop.