Barmouth or Dolgellau? Both great places – enough for the family to do whilst you pedal off into the distance. Used to live in North Wales and holiday there most years. Seem to find that if you stay by a beach, the driving is self limited as some days you just don’t have a need or inclination to go anywhere. Stop inland and the weather turns, you spend all bloomin’ day driving and the kids get fractious.
Dolgellau has a great children’s playground, plus bike hire right in town. And of course just up the road from there……
Another option is Beddgelert, which provides easy access to Snowdon of a morning before everybody is up. Steam trains and ice cream for kiddo. Job done.