2 or 3 nights getting from Holyhead to Bath

Yes, it is doable. When going from Portmeiron area to Hay, you may wish to take A496 route and go via Harlech to see the castle - then on down to Barmouth and continue on A496 alongside the beautiful Mawddach estuary towards Dolgellau. (If you just want a faster route - take A487 and A470 to Dolgellau. (Dolgellau is a town built of huge blocks of stone).

From Dolgellau southward - it is the A470 - which is a very scenic route through the middle of Wales. However, it has a lack of washrooms / toilet facilities. That being so, you make like to consider stopping at the Burger King - which will be on your left before you cross the river at Builth Wells - or use the nearby supermarket. At Lyswen - turn left for Hay.

On day 2, leave Hay on B4350 to Three Cocks and follow signs for Talgarth to join A479 skirting the Black Mountains to Crickhowell and on to A40 to Abergavenny. A complicated double roundabout is found S of Abergavenny. I suggest you take A40 expressway going E to Raglan - where you can take a HARD TURN left into the castle car park.https://cadw.gov.wales/visit/places-to-visit/raglan-castle

From Raglan, you could take A449 expressway south to join M4 just E of Newport and then over the Severn into England. Alternatively, you could take some NARROW back roads going south east wards from Raglan village towards Chepstow and then cross the Severn estuary on the M48 bridge.

Another way to proceed from Raglan would be to stay on the A40 expressway to Monmouth - where you loop around at a roundabout and turn left at traffic lights for the lower Wye Valley on route A466 This will bring you to TINTERN and the ruined abbey. On reaching CHEPSTOW, you could divert through the town and down the hill to the castle or just stay on the A466 until you reach the M48 to cross the Severn Bridge to England. https://cadw.gov.wales/visit/places-to-visit/tintern-abbey
https://cadw.gov.wales/visit/places-to-visit/chepstow-castle

Once in England, you will be on the M4 and need to leave at junction 18 for the run down the A46 into Bath. In the event that you arrive in this area early, you may like to consider visiting :> https://www.nationaltrust.org.uk/visit/bath-bristol/dyrham-park - which is about 2 miles south of the M4 junction 18 on route A46. You are now very near to Bath so it might be better to pop back on one of your Bath days to give this place more time.

Note that a sign with a diagonal black bar means that you can drive at the national speed limit for that road. Where a road has a lane in each direction - like most of the A470 - it means you can drive at up to *60mph. Where a road is dialled with a central barrier - the speed limit is 70mph *unless a lower limit is shown.

You may like to know that you could have done a similar journey by train - but not via Hay. This You Tube British TV documentary shows you the Cambrian Line from NW Wales to Shrewsbury.

Thank you, James! For all the suggestions and links!

You would probably need about half a day in Portmeirion. You may find that you can't fit it in on day 1 and have to do it on day 2 before you head south to Hay.

In the event that you go to Llandudno on day 1 - try and also include Conwy - which has a medieval castle. Also note that Bodnant Gardens is not far off the A470 route which you would use to Betws-Y-Coed in order to get to the Porthmadog area. You certainly won't be able to do Llandudno, Bodnant and Portmeirion all in one day.

The most scenic way from Betws-Y-Coed to the Porthmadog area is A5 to Capel Curig > A4086 > A498 to Beddgelert and through the Aberglasyn Pass to Porthmadog. Do look at these roads on Google street view to see what they are like!