Charles
Agree with Thomas that late-April to mid-June, or alternatively September to mid-October (when British Summer Time ends) are the optimal windows for a golf trip to Wales
If you are flying into Manchester, and ending up at Bristol, then you probably want to base yourself in three or four natural centres, viz Llandudno, Harlech, Swansea and Porthcawl
First, try the Victorian resort of Llandudno, a good base for North Wales GC and Conwy (2020 Curtis Cup venue)
From there, you can drive via Nefyn across Snowdonia down to historic Harlech, which can be a base for both RStD and Aberdovey (and going from the former to the latter by train remains one of the great seaside journeys in golf, with some fabulous estuary views: the Aberdovey clubhouse is practically an extension of the station platform).
You could then do the longish drive south from Harlech via Borth and Ynyslas or Cardiganshire (Gwbert-on-Sea) to South West Wales, and have a Swansea base for Tenby, Ashburnham and Pennard, before heading on to Porthcawl, as your final centre for Southerndown, Pyle and Kenfig and RPGC itself, before the concluding two and a bit hour drive from Porthcawl to Bristol Airport.
The only problem with this seagirt itinerary is that you don't take in some of Sean Arble's inland gems in the hills of the Welsh Marches like Llandindrod Wells and Welshpool and Kington, but in some ways it's easiest to combine those with the English Midlands: certainly a tour that took in (say) Little Aston and Welshpool would run the full gamut of the UK golf club experience!
Of course you won't (I suspect) want to visit all of these, and I would always recommend 36 holes at one course on a single day rather than trying to do two different courses on the same day: much less driving, time for proper lunch and a drink, and very often much cheaper too. Whatever you do, though, you should definitely try to get on to Harlech, Aberdovey, Pennard and Porthcawl, not least so that you can then join in the friendly jousting about their relative merits on GCA! The other point Thomas and I always emphasise on this site is that driving times in Wales can be much greater than you think: it's possible that after you have left Llandudno you won't encounter a single further mile of dual carriageway highway until you get down to Swansea!
Jim Finegan's book on England and Wales All Courses Great and Small is excellent pre-trip reading, whatever you decide, as are the essays on Aberdovey and Harlech in Patric Dickinson' s A Round of Golf Courses. Bernard Darwin (a former President of the Welsh Golfing Union) spent more holidays in Wales than anywhere else, so you'll be in very good company...