Dubh Linn:
Kehoes
St James Gate
Jameson Distillery
Trinity College (mainly the library)
Temple Bar
Kilmainham Gaol
St. Patricks Cathedrale
General Post Office (or better yet, take a 1916 rebellion tour)
Or just go native, hit some public houses and wonder about.
Can't help you on London.
Whitey, I have a picture of the GPO and a picture of Michael Collins on my desktop. It's a good reminder of things.