I completely agree with Duncan about the Missing Links website, which is a source of endless pleasure (and seems still to have information and images added on a regular basis - see e.g. the entry for the much-missed Bramshot).
Missing Links also has much to say about the only other royal club to have ceased to exist (hitherto, anyway), namely the celebrated Royal Isle of Wight Golf Club on the Duver opposite Bembridge: indeed such has been the interest in this organisation (the specialist subject of the distinguished British golf historian and collector Philip Truett) that a wholly new history has been commissioned - remarkable really for a golf club that expired nearly sixty years ago. It is also now possible to rent out and stay in The Old Club House of the RIoWGC, a National Trust pavilion property.
As for Royal Cornwall, it was the venue for the very first Cornwall Amateur Championship in 1896, and for the very first Cornwall Ladies' Championship in the same year: the latter returned on three further occasions, lastly in 1910. As a course RCGC was clearly never held in anything like the same esteem as Bembridge, and the royal connection was indeed through the Duchy: neither Bodmin Moor, Exmoor or Dartmoor has ever proved particularly fertile golfing ground, with the exception perhaps of Moretonhampstead on the edge of Dartmoor, the Abercromby course of 1926 known nowadays as Bovey Castle and emphatically worth a detour (warmly endorsed by Henry Longhurst) for any GCA readers in search of an appealing stopover en route to or from St Enedoc or Westward Ho!