I’m going to say Arthog nr Barmouth.
Why?
The lovely Mawddach Trail all the way to Dolgellau, easy level family cycling in stunning location
Lots of seaside interest, great pub (George III at Penmaenpool)plus a few good ones in Barmouth via a walk across the railway bridge over the estuary from Arthog
Still quiet enough to feel like you have spots to yourself
Supermarket at Dolgellau
The Blue Lake, via an adventure exploring the old quarry, tunnel, etc looks like giants have been building up there.
Cader Idris
Miniature train for parents and toddlers at Fairbourne.
Coming up short with swimming pool unless you swim in the ocean. There is Barmouth Bay Holiday Park with a pool.
We booked a nice cabin there recently and it was top notch, have been to Arthog many times, but mainly grown-up walkyclimbybikey stuff so kids might be better served in Barmouth. You can bikeover the railway bridge too, my favourite morning jaunt is the 6 miles on the level trail to Robertses cafe in Dolgellau. Grab a few groceries from supermarket, then a leisurely ride back, catch lunch in Penmaenpool go visit the RSPB, take binoculars.