The local castles may be more fun in the sun but rain doesn’t stop the more intact castles such as Caernarfon (or to a lesser extent, Conwy and Harlech) from being interesting days out.
Inigo Jones slate works, Penygroes, on the way to Caernarfon.
Slate caverns, either at Llanfair near Harlech or Llechwedd near Betws-y-coed
Copper mine, Beddgelert.
Pili Palas, butterfly farm, Menai Bridge area.
Anglesey Sea Zoo, is a bit of trek as it is on Anglesey so best as part of a full day out in the area.
Airworld Aviation Museum, Caernarfon.
GreenWood Family Park, Y Felinheli, has plenty to do indoors, though better on a nice day.
Ty Gwyn Arts Cabin, Morfa Nefyn.
Pwllheli arcade, not the fun fair I remember from childhood, but the kids still seem to enjoy it.
Cinema Neuadd Dwyfor, in Pwllheli, has recently been renovated, and the library is open.
Maritime Museum, Nefyn, in the old church.
Porth y Swnt, gallery and local history museum, Aberdaron.
Plas Tan y Bwlch is a manor in a dramatic setting with an interesting history. In wet weather it is a nice spot to break a journey and learn about the history of the area.
Harlequin Puppet Theatre, Conwy.