Dear biglips, if you head for Anglesey, Moelfre and Llugwy are lovely beaches and great for children. On rainy days there is the Sea Zoo at Brynsiencyn, the Pili Palas (butterfly house), Oriel Llangefni ( a lovely small museum and gallery) and plenty more.
Another good beach option is Dinas Dinlle, just out of Caenarfon, heading for Pwllheli - there is a family friendly site down there and the beach is ideal for children when the tide is out. Abersoch is another option, it's lovely but does get very busy.
If you prefer the mountains there is a sweet site at Dwygyfylchi which is just above Conwy - a good town to explore with a wonderful castle - and a very scenic site on the Capel Curig side of Bethesda, next to a river and a beautiful waterfall.
The areas around Penrhyndeudraeth (near Portmeirion) and Harlech are also stunning - Harlech has a 7 mile sandy beach and a fantastic castle.
Avoid Rhyl, Prestatyn and Abergele!
I hope you have a lovely time.