Matthew,
I agree with most of what has been said but for what it's worth, and as I have a spare 20 minutes, here are a few recommendations and photos:
Nefyn - Having spent a week in each of the last two summers, and already booked for next year, in a cottage in Nefyn, I need no persuading about the beauty of the place. It is worth visiting, as the 'old' 8 peninsula holes (you must play the 'old course') are unlike anything you have seen, or will ever seen. It's a bit crazy - the 12th is mind bogglingly mad, but the views are sensational. If you're confused, you can pop down to the Ty Coch Inn ('Red House') after the 12th or 15th for a pint or two. The 13th is in the upper reaches of the finest holes I've played, but the course conditioning is basic.
Royal St. David's - For such a beautiful setting, it doesn't really have a great deal of charm. It's a great test of golf, and the bunkering is first class, but it seems like an opportunity wasted. The dunes are massive, but the course rarely penetrates them. Well worth a visit though, and make sure you visit the castle as the views are fantastic.
Aberdovey - Lovely place. The Dovey Inn is a brilliant place to stay and teh course is very good. A bit flat and uninteresting in places but a lot of good holes and well worth seeing, particularly if you are playing RSD and Nefyn.
Aberdovey and Tenby or Pennard are very close geographically but the drive will take hours due to the windy roads. If you want to see SW England, particularly Cornwall, then limiting yourself to South Wales is probably best on a short trip. I would recommend this as St.Enodoc is simply a must.
Tenby is the furthest outpost of good golf in South Wales, about an hour west of Pennard. It is a lot of fun, and the town is very pretty (as long as you don't go in August when it will be packed). Ashburnham is on the way from Tenby to Pennard. Scandalously, as it is about 2 miles from the village where my mother grew up and that I have visited hundreds of times, I have never played it. Pennard is fantastic and should not be missed. Wild, windy, and in pretty ropey condition, it is a fantastic design. You will not be disappointed.
Porthcawl, Southerndown, and Pyle & Kenfig are all very close together and conveniently located just off the motorway back into civilisation (England). I have only played P&K which has a brilliant back nine, and a very average front nine.
Burnham & Berrow is another superb links and, again, is very conveniently located just off the motorway down to Cornwall. Given it's convenience it is very difficult to come up with a good reason not to play it as it is first class.
Of the courses in the SW of England, St Enodoc is undoubtedly the highlight. It is in my handful of favourite courses and is simply magical. The views are superb, the course is challenging, quirky, beautiful, and fun. What more do you want? Play it more than once - stay in Padstow, eat fish and chips from Rick Stein's chip shop (out of this world!), play St. Enodoc. Fantastic!
Saunton is really high class golf, with two wonderful courses. A must and very close to Royal North Devon, which is a museum piece.
I would skip Trevose and head to Perranporth which is an absolute blast. Completely unfair but great fun it is not 'high class' but you will enjoy it as much as any other round you play on the trip.
Enjoy!