In reply to Bobling:
Always enjoyed exploring the coastline on Anglesey with the kids (northern coast is overlooked). Little bays & beaches to explore. Though never been to Anglesey in high season !
Paris Mountain (old mine area) is also worth a trip if your kids like that sort of thing.
And Newborough (can be quieter away from busy car park. Plus there are some biking trails) and walk out to Twr Mawr LHouse.
Rock pooling at N End of Trearddur (can be busy) and kids body boarding/beach at Porth Dafarch (little bay/beach to N of Trearddur).
Back over on mainland, also Penrhyn Castle and Caernarfon Castle give further wet weather options.