It completely depends where in Cornwall you move to. There are villages that are dead 10 months of the year, and villages with a lively, thriving community. There are towns that are really depressed, towns that are expensive and full of DFLs, and towns with a buzzing student scene.
It really makes me laugh when people say there's no culture here- they don't look very hard, do they?! 😆 Check out the Redruth Drapery, the Poly in Falmouth, the Cornish Bank in Falmouth, the Acorn in PZ, the Old Bakery Studios in Truro, etc etc... over the last year I've heard banging acid techno, black British folk music, Gruff Rhys, I just missed out on tickets to General Levy the other day, I'm going to see Attila the Stockbroker next weekend, saw an amazing one man show last weekend at the arts centre in my actual village, saw an exclusive preview of Empire of Light at the Falmouth film festival, participated in the Montol midwinter parade and general lunacy in Pz.....and that's as a single mum who can't get out much, there's way more going on that I can't get to!
With teens, I'd try and find somewhere close to a station. Then Falmouth, Truro (for college), Penzance, Plymouth, Newquay are easy for them to get to. (I'm in a village. DS1 has made sure that every single one of the friends he's made at secondary lives on the exact opposite side of the catchment area, 30 mins drive away. It's excruciating).