Cardiff Stay

St.Fagans Castle & Museum - allow half a day.
Castell Coch and Caerphilly Castle - allow half a day.
City Centre plus Cardiff Castle - 3 - 4 hours. Add on time if you wish to visit National Museum of Wales - art galleries, geology of Wales, flors and fauna etc.
Cardiff Bay (Waterfront area 1 mile south ion city centre) - can be seen in 1 hour but allow longer if using boat from landing stage in Bute Park (park on west side of castle).

If you are driving north on route A470 through the middle of Wales, note there is a lack of toilet facilities. First good place to stop would be Brecon Beacons Mountain Centre - hard left onto minor road at Libanus (first village when descending from Brecon Beacons).

Note that route A470 takes a hard left turn a few miles east of Brecon.

A Builth Wells, a cafe with toilets is found just over the river bridge - on right.

Great suggestions from James - but I needed a full day for St Fagans as there was so much to see there!

There is also Llandaff Cathedral and what about a ghost walk? Check out either here or here.

Barry Island with is sandy beaches and holiday atmosphere isn't far away.

If you like stately homes, Tredegar House (National Trust) isn't too far to drive.

Plan for three nights as there is plenty to do!

Thank you again for the information. More questions as I try and organize this leg! Is it reasonable to drive Cardiff to Llandudno all in one shot? Would it leave time to stop in Brecon Beacons for a good look around? If not where would you stay for a night?

The Brecon Beacons National Park runs a good way from east to west but not so far south to north - so, yes, you could see the Brecon Beacons whilst driving to north Wales but would not have time to climb to the summits, visit the waterfall country, the National Showcaves of Wales, the Black Mountains to the east or say Carreg Cennen Castle on the western side. I would suggest you stick to the A470 until you reach the first village (Libanus) on the descent from the BB and take hard left. After about 8 minutes you come to the BBNP Mountain Centre. Use toilets have coffee etc. and walk onto moorland to take in the view of the BB.

Driving from Cardiff up the A470 (not accounting for any stops and driving as fast as possible), I have reached Builth Wells in 1 hour 30 minutes; Rhayader in 1 hour 45 minutes and Dolgellau in 3 hours (124 miles from Cardiff). Dolgellau to Llandudno would take I guess almost another 2 hours - so yes, it can be done in a day but that is pushing it and not really leaving anytime for sightseeing and you are unlikely to match my timings. The road is very bendy going through hilly/mountainous terrain. Most is not dualled highway.

I would consider staying a night at Dolgellau or take a detour here and drive down the beautiful Mawddach estuary to the seaside town of Barmouth for an overnight. That would then allow you to take the coastal route the following day to Harlech to see the castle before heading on to see Portmeirion before continuing your journey to Llandudno.
When staying in Llandudno, try and visit Bodnant Gardens:> https://www.greatbritishgardens.co.uk/conwy/item/bodnant-garden.html

PS. I would not bother visiting Barry Island whilst in Cardiff.

There is a lot more to see in South Wales than Cardiff.

We loved Tenby and St. Davids as well as several castles.

Once again I appreciate all the comments!