I am going to imagine I am showing someone who knows nothing about British mining as much as possible in two weeks. I would want to take them on a journey through time from the very beginning of mining to the 20th century.
I would start high on the Sussex downs, at Cissbury Ring, where there is plenty of evidence of neolithic flint mining, and its a beautiful place on the chalk downs with an impressive hillfort. Then a visit to the Anne of Cleves Museum in Lewes to see the Wealden Iron display, iron having been worked extensively in roman and pre-roman times in Sussex, Kent and Surrey. On the way to my next site, I would stop off in Crawley - well, I live there - and there are ancient medieval mine pits right behind the civic theatre, and one of the earliest tudor gun furnaces in the forest a mile or so away. My first underground site would be the medieval stone quarries in east Surrey, following the historical theme, as economically, stone extraction is a largely forgotten and important part of the economy of the middle ages. Unfortunately, this is not a show mine so we would have to be content with exploring the surface pits, but we could pop into Reigate Caves where we could see a few displays on the local mining and quarrying industry, as well as seeing some sand mining.
That covers flint, iron, sand and stone, and we are probably only into day 2!
Now its time to head west, but before spending several days in Cornwall, let's stop off in Dorset to see the Purbeck cliff quarries which have some underground elements but which are a spectacular surface site. This is probably the best we can do instead of the Wiltshire quarries as none of them are museum/show sites.
To appreciate the scale of post-medieval metal mining (from the 18th century onwards) there is plenty in Cornwall - Levant and East Pool most definitely. I might also venture high onto the moors - either Bodmin Moor or Dartmoor to find old streaming sites of note. Where would you suggest?
Now it's time to move on. Coal is the next subject, and for this we need to pop round into Wales. Big Pit cannot be missed out. Dolaucothi for gold! A brief digression back into England to Ironbridge - the story of iron cannot be told without a visit here. Onwards back into Wales to Blaenau Ffestiniog. Plenty of surface stuff to see here! Only worth going underground if you can avoid the Male Voice Choirs (?).
The Peak District Mining Museum, and a visit to Magpie Mine will show that there is more to metal mining than Cornish tin and copper.
Have we had enough of coal? If not, try Caphouse Colliery.
Nenthead and Killhope, I agree, are excellent places to visit, but now I suspect we are straying too far and must return to civilisation. Back southwards then!
Before completing our little holiday, my new friends should be reminded of the antiquity of British mining, and a stop at Grimes Graves to see the flint mines is in order. Finally, London! Here we can visit the Science Museum to look at the early steam engines preserved there, and call in at Kew to see the beam engines.
Howzat?