We will be there for a day in May. I would appreciate any recommendations of places to see or explore.
Plas Newydd, Beaumaris Castle (possibly the greatest of the Edward I castles), Caernarfon Castle, South Stack Lighthouse, Bodnant Gardens (only an hour by taxi from Holyhead).
You are not allowed to walk off the pier (if using the normal cruise ship berth)- a free shuttle bus will take you into town where you will need to rendezvous with whatever transport you are using.
Have you looked at the excursions offered by the ship?
In addition to what has already been mentioned, there are a number of ancient standing stones and burial chambers around the island, e.g., Trefignath, Penrhos Feilw, Bodowyr, Bryn Celli Ddu, etc. The Melin Llynon, (windmill) Llanddeusant was a nice visit. There was an on-site tea room and pastry shop right there. There’s also the town with the long name, Llanfairpwllgwyngyll… There isn’t much there except a store and train station, but was still fun to visit.
How you’re getting around will make a difference in what you can see in the time you have.