The Four Courts, Dublin
Rainy days are a great incentive to explore Dublin's interiors, and the risk of alcoholic addiction dictates that at least some of this exploration should be conducted in premises other than licenced ones (though we won't fault you if you don't stick to such a heartless dictum!).
As a city we are blessed therefore to have a wealth of opportunity in this regard. Three cathedrals, civic offices which are the product of architectural genius embodied in the likes of James Gandon and William Robinson, and numerous other nooks and crannies which offer way more than mere respite from the odd shower!
The range of experience varies from the classical opulence of Gandon's Custom House and Four Courts to the hectic energy of the Fruit Market on Little Mary Street, and from the medieval hush of Christchurch Cathedral vaults to the equally spiritual ambience of the great glasshouses in the Botanical Gardens, Glasnevin.
Some places are less well known but equally rewarding. Collins Barracks near Heusrton Station is now a branch of the National Museum but is worth a visit for its 18th century cloistered quadrangle alone. Quite different in nature but also worth a visit is the Irish Waterways Interpretative Centre, built on stilts over the water of the Grand Canal Dock off Pearse Street.
The list goes on, and space here does not permit a fully comprehensive listing. But be aware of the most important thing, whichever of these places might take your fancy - all the sites listed above are free to enter!