Caernarfon should definitely stay as the city in NW Wales. It was the capital of Gwynedd and was an important city in the area long after the English conquest.
Caernarfon was never the capital of Gwynedd - it was founded by the Normans who built the castle after their conquest of Wales.
Deganwy was the capital of Gwynedd at the start time of the mod, and it had moved to Abergwyngregyn (modern day Conwy) by the time of the Norman invasion.