Cornwall’s a big old county (ok, a long old county) so you might want to pick one specific part. Penwith (far west) and the Lizard are both very different from the rest of Cornwall, and from each other but I love them. There aren’t especially full of “attractions” per se but if you’re happy just to be outside, the walking / swimming / beaches are fantastic.
People have mentioned the Minack, the open air theatre at Porthcurno. Really should be on your list, but check their website for opening times (or better yet, ring them when your down here). They have matinee performances on Tuesdays and Thursdays, as well as kids shows on Wednesday and Friday mornings in the season, so you can’t rely on just turning up and getting in. There’s also a real gem of a museum at the bottom of the hill, telling the story of how Porthcurno was the silicon valley of the earliest telecomms technology. Re-opening after a major refurb in June (www.porthcurno.org.uk).
The Penwith moors are also good for rambly walks, specially if you’re into you prehistoric stuff. There are loads of random stone circles, ancient sacred wells and the like – try googling Men-an-Tol.
Are you aiming to get any riding in, as that could influence what part of the county you aim for?
ETA: Roskilly’s Ice Cream farm (on the Lizard) is a fun half day out if your youngster is the right age – needless to say it’s got a great cafe too!
If you’re used to driving in Scotland, though, be prepared for a lot more traffic, most of it being driven very slowly and in a slightly lost, hazy fashion! All part of the experience, you just have to go with it, I’m afraid!
