The first site I remember was Grey Wethers, which I visited not long after we moved to the other end of Devon in around 1978/9. Dartmoor in winter was a great place to go for a long walk with kids in those days... maybe they'd not be as interested now with modern distractions!
(Our real 'first site' was Cow Castle on Exmoor, when we lived in N. Devon, but am not sure if it has the sort of 'extant' remains you meant.)