I think all those places will be quite expensive; are you in the National Trust, as Members get in 'free'?
In DEVON: Dartington Hall gardens (near Totnes) don't charge, but do ask for donations, and car parks are charged.
NT gardens: Coleton Fishacre ; Greenway (Agatha Christie's home); Overbecks, Sharpitor near Salcome, has 'secret' rooms for children.
Dartmoor is rugged and free.
Two steam railways: Paignton to Kingswear, along the coast; Dart Valley, beside the river Dart from Totnes or Buckfastleigh.
In CORNWALL: Land's End, many people say is a 'rip off'' - expensive and just like all the rest of the lovely Cornish cliff tops! But you can park elsewhere and walk along the cliff top to get to it.
Porthcurno has a Telegraph Museum, as the first Trans Atlantic cable went form there, and there are wartime underground rooms I think.
Porthgwarra (the 'cave' in the recent Poldark), Treen, Porthchapel and Penberth Cove are all on the Land's End peninsula, and there is a web site of ALL the Cornish beaches with full details of each one.
The Lizard has the Goonhilly Earth Station, satellite communications etc. And lovely coves and beaches.
St Michael's Mount is NT, and at low tide you can walk across the causeway.
If you Google you can find all these places on the web, and in Street View you can have a 'virtual walk' around many of them.