Irish Whiskey is Rarely peated, but some are. Connemara is the most notable (and delicious) example that is, particularly their 12 year. If you are tasting smoke in irish whiskey it is likely a result of the barrel. Some distilleries (both scotch and irish) recycle used american bourbon barrels. The inner charring of the barrel may elicit some minor smokey taste.
I would also recommend Greenore for an unpeated excellent irish. And the only really good Jameson, the 15 year pure pot still. For barrel aged "scotchy" examples, although they more resemble speyside scotches due to the barrels they are aged in, try Tyrconnel's Sherry and Madeira barrel aged offerings. They are far superior to their mediocre flagship bottle.
If you do like a lightly smokey flavor, lowland scotches are very mildly peated. Try Glenkinchie and Auchentoshan for good examples. Scotches from NORTHERN Islay are also mildly peated, such as Bunnahabhain and Bruichladdich. Read up on those though, because those distilleries also have offerings that are peaty as hell, similar to their southern Islay neighbors. There is also Japanese whiskey, which is basically unpeated scotch. Yamazaki, Hakushu, Nikka, and Kirayoshi all make fine offerings.