You've got to have a boxty!
http://boxtyhouse.ie/
That place is very popular with ABers. It's in Temple Bar which, as EdmundD, suggests, is at the heart of Dublin's eating & drinking scene:
http://grev.eu/wp1/
The Guinness Storehouse is, by its nature, a bit 'touristy' but it's still worth a visit (even if only for the fantastic view from the Gravity Bar):
http://www.guinness-storehouse.com/en/Index.aspx
I'm not normally a fan of the open-top bus tours that every tourist city seems to have. (I usually prefer to explore on my own). However Dublin's attractions are quite well spread out and I'd recommend using the hop-on/hop-off buses:
http://www.dublinsightseeing.ie/citytour.aspx
There's lots more on the city's official tourism website:
http://www.visitdublin.com/home/
and Wikitravel:
http://wikitravel.org/en/Dublin