In reply to Scruffy:
Eaiest access to both top and bottom is probably Trewavas, near Helston, but you're looking at about an hour's drive from Mawgan Porth. However, it's a good choice for beginners: a decent selection of VD and S, shortish single pitch, of which most can be simply set up as top ropes (assuming you have some rigging rope). Rinsey Cove is nice, and Praa Sands is also nearby, if you wanted to factor in a beach.
At Bosigran, Alison Rib is a popular choice for beginners (but you'd have to lead it as it's two pitches). Sennen is both further away and more complicated to get to the crag base - there is a low tide walk in, otherwise it's gully scrambles or abseil. There are some good lower-grade routes there, but FWIW I'd prefer to take people with one or two sessions under their belts, and perhaps not complete first-timers.
If you did want to introduce the family to a few skills in advance (not a bad idea, especially if considering Bosi/Sennen), there's one or two indoor walls not too far away. Granite Planet in Penryn would be a drive of 45 mins or so, and I believe there's a small wall at a sports centre in Newquay (only intermittently available), which would probably be your closest. Could be useful if it rains, anyway.