Hi Colin.
I agree with Jonathan about the Nantlle Ridge. I’ve done that with my MTR. It’s a great hike.
But if you get good weather for a lovely day out with the family I’d suggest Bardsey Island. Please see this thread.
I have a page on my blog that covers most of Pen Llŷn as well as the one on Bardsey.
One I’d recommend for a gentle day with the family, especially if the weather is good, would be to do Garn Boduan in the morning, and then head to the beach at Morfa Nefyn, with lunch at Tŷ Coch, further along the beach. It’s a sheltered bay and can be quite scorchio (for Wales) in the summer, and thoroughly pleasant in springtime.
Of course if you want a train ride I am bound to recommend the Welsh Highland Railway from Caernarfon to Porthmadog! Whilst it doesn’t take you directly to a SOTA about half-a-dozen are along the way. You might take it as a route planning exercise whilst enjoying a beer. 
Simon