Charles,
One of the best ways to play a variety of courses in the UK is to play in club open competitions. Virtually every club has them, except maybe the super-exclusive ones.
There is a website called Golfempire which shows all the open comps categorised by club, by county, by date, etc - see -
http://www.golfempire.co.uk - there are both midweek and weekend open comps. I believe others from the US posting on this site have followed the open comp approach with success.
By interrogating the site you ought to be able to put together an itinerary of clubs/courses to play. You can book many of the open comps online with links via the Golfempire site and you'll play with others who have also signed-up for the comp. Open comps are also normally cheaper than regular greenfees and you might even win a prize. On days with no open comps to play in you can always play greenfee golf if you desire or do Devon/Cornwall 'craic' kind of equivalent or touristy type things.
Devon/Cornwall being a long, thin peninsula travelling from one side to the other is possible but if you stay on one coast it can take quite a while to get to the other coast, obvious really, but by basing yourself more in the centre of the peninsula you can reach either coast quicker, if you get my drift.
As to timing, be aware that in the UK at the end May/early June the schools are on holiday for a week or so so accommadation, roads etc all get busier and a prices sometimes adjust accordingly. You should be able to find and thus avoid the school holiday dates with a bit of web-searching.
The bigger name courses like Saunton, Westward Ho!, St Enodoc etc etc speak for themselves. As to some slightly lessor lights definitely play clifftop/links at Perranporth, once played never forgotten, and as mentioned in my earlier post, moorland Yelverton.
Hope this helps.
Atb