Depart LAX overnight on a direct flight to Dublin — flight time ~11h30m; you cross time zones and arrive next day local time. Overnight flight saves a day of travel and gets you into Dublin in the morning.
Short walk from Trinity; Dublin Castle grounds and the Chester Beatty collection (usually open ~9:45–17:45) are good introductions to Irish history and art.
Catch the Stena Line ferry from Dublin Port to Holyhead (approx 3h30m); schedules vary through the year so book an evening crossing to reach Wales this evening.
Explore Snowdonia National Park — short walks from Llanberis or a scenic drive; Snowdon Mountain Railway sometimes closes in winter, so check seasonal status before booking.
Choose the atmospheric Jorvik Viking Centre (timed entry recommended) or the free National Railway Museum; check opening hours (typically ~10:00–17:00).
Short drive or tour to Urquhart Castle and Loch Ness (castle typically open ~9:30–17:30); boat tours of the loch run most of the day but check seasonal schedules.
Short walks or viewpoints around Fort William; if you prefer, ride the Jacobite Steam Train (seasonal, check availability) or visit the West Highland Museum.
Evening ferry to Belfast (check seasonal schedules; crossing ~2h15m); arrive in Belfast late and transfer onward to Dublin by train or evening transfer.
Enterprise train runs Belfast–Dublin (~2h10m); you may arrive in Dublin late — consider an overnight stay in Dublin to catch your return flight next day.