For cask? Well post-pandemic there's a lot less choice than there used to be, which was very little anyway.
Any of the Galway Bay Brewery bars will be great for general craft beer and they tend to have a cask or two on the go. Black Sheep can have 2 or 3 going.
Porterhouse doesn't really do cask any more but worth popping in for their own beers and any guest beers they have on. A great example would be go to Porterhouse Temple Bar and Beer Temple a few doors down. Beer Temple is great as you can pick the modern bar side or the older wood bar side (The Oak). I don't think they do cask in there offhand.
One of our favourites, Underdog should be re-opening at a new location in a couple of weeks at the former Legal Eagle so if you're lucky, you might get to visit.
Be sure to get out of the city centre, 15-20 minute walk to our good friends at 57 The Headline and support them. I recommend going for a SMASH burger and a pint of Trouble Ambush but there's plenty on offer there.
The Big Romance usually has a few interesting beers on so it's certainly worth a visit.
And purely for cask, without wanting to start any booing, the few Wetherspoon pubs might be worth a try as they have Irish cask on from Dungarvan and Brehon roatating these days, there might be another Irish brewery there too.
There are plenty of regular options, it's hard to find a pub in Dublin that doesn't have some local craft on but cask is very hard to find. Anyone know if The Palace Bar still has a beer engine going? Worth popping in to check anyway, if it is, it's right by the door.