These are all places I have used personally: -
www.dunnesstores.com
Dunnes is great, good range from their own reasonably priced range to fashion and home designers like Paul Costelloe, Carolyn Donnelly, Francis Brennan, Lennon & Courtney and many more. Homeware section is excellent. They also deliver to the UK (and beyond).
www.easons.com
Ordered from here recently, very prompt delivery. Be sure to sign up for email offers for discounts
www.blarney.com
Beyond the touristy stuff, they have lovely throws, got one two years ago Avoca brand and another just lately, very prompt delivery, lovely quality. Be sure to sign up for email offers for discounts.
www.kilkennyshop.com
Be sure to sign up for email offers for discounts otherwise a bit pricey.
There's a Facebook group called Shop In Ireland, they have a website too (www.shopinireland.ie) possibly like how Etsy was in the old days, lots of individual sellers - I can recommend this seller - www.shopinireland.ie/product/superhero-frame-with-marvel-border-female/
www.cocomochocolate.com
Wonderful artisan chocolate
lilyobriens.ie
More chocolate but on a larger scale, we got their Advent Calendar last year which I refilled with chocolate this year.
www.kennys.ie
A truly wonderful selection of books from an independent store, possible to get signed editions etc, delivery just a little slow at the moment.