travel by ferry Llangollen to Belfast or Dublin
I looked into that same journey for a trip this summer. It's a couple of hours by train or bus/train from Llangollen to Liverpool, then an 8-hour ferry ride from Liverpool to Dublin. I decided that's not how I want to spend a day of my vacation, so we're flying instead. But you can check it out for yourself here: P&O Ferries
You don't say whether or not you are hiring a car. If you are, I would suggest that you follow the A5 west out of Llangollen and follow it all the way to Bangor - through the Snowdonia National Park. (It is very scenic). Then join A55 expressway to cross Anglesey to the ferry port of Holyhead.
If you don’t have a car - take a bus from Llangollen to Ruabon - where you can catch trains (hourly) to Holyhead.
www.nationalrail.co.uk (You can buy a combined rail & ferry ticket).https://www.arrivatrainswales.co.uk/SailRail/Why/
Irish Ferries & Stena Line operate the ferries on the shorter sea crossing from Holyhead to Dublin.
I take it that you know that the wonder of the Victorian age is just a few miles east of Llangollen? :>https://www.pontcysyllte-aqueduct.co.uk
You may also like >http://llangollen-railway.co.uk