A week in Wales

Cardiff and St. Fagan's and Caerphilly castle are easy to do with public transportation.

Here is a map of rail lines in Wales, so you can see what towns and villages you can reach by train.

https://tfw.wales/sites/default/files/2022-02/TfW_Network_Map_ENGLISH.pdf

When people suggest places to visit, you can use this plus the National Rail.uk journey planner to look up routes and connections.

Conwy, for example, on the line across the north of Wales between Chester and Holyhead, has a nice castle:

https://cadw.gov.wales/visit/places-to-visit/conwy-castle

But I am sure people can suggest others.

I would stay in Llandudno (pronounced Clan-did-no). It’s a genteel seaside town, so lots of accommodation options. By train, you can easily get to Conwy and see it’s castle, the old walls and buy fresh muscles by the harbour.

Other train trips from there include Chester, Anglesey and Snowdonia for rural communities and a ride on the Ffestiniog railway.

The area north of Cardiff is former coal mining communities and not as rural as the north.

Llandudno or Conwy would work well, and you could easily spend a week based there. They are close together and have good bus connections to other parts of Wales. You may find Llandudno Junction a better train stop than Conwy. It is just a short taxi ride from Llandudno Juction to Conwy.

You could easily spend a full day in Llandudno (Victorian Tramway, Great Orme Copper Mines, seaside... ) and another full day in Conwy (ruined castle, town walls, Plas Mawr ...)

Catch a bus to Caernarfon for the castle, or get off before and spend the day at Penrhyn Castle, if you have seen enough ruined castles!

Use the Conwy Valley railway line for places like Betwys y Coed and Blaenau Ffestiniog (Llechwedd slate Caverns and activities). Blaenau Ffestiniog is the terminus for the Ffestiniog Railway. Check the timetable as it may be possible to do a round trip. If not, the half trip to Tan y Bwlch and back is still worth doing.

Spend another day catching a bus to Beaumaris (castle and goal)

Catch the bus to Bodnant Gardens

As you are coming down from Scotland, I would suggest that you do north-west Wales. Train from Glasgow or Edinburgh to Warrington or Crewe where you change for another train into north Wales. It may be cheaper to split the ticket(s) and these sites will tell you:>
https://www.traintickets.com/?/
https://trainsplit.com/

Also note that buying long distance train tickets on the day is dearer than buying Advance tickets for specific trains. However, if you try and buy too far in advance, you may find ‘journey can’t be made’ or high prices. (Usually, the journey can be made but they have not loaded the prices for Advance tickets. I have just checked on train tickets.com for mid March Glasgow to Llandudno Junction and found prices around £40 using split tickets. (That is without a Railcard which would get you about a third off the fares).
https://www.railcard.co.uk

Here are 2 narrow gauge scenic railways that will take you through the Snowdonia National Park:> https://www.festrail.co.uk
In southern Snowdonia, the ‘normal’ Cambrian Line is also very scenic but you cannot open windows to take photos. This line turns inland eventually to cross mid Wales to reach the English border town of Shrewsbury with the train continuing to Birmingham. https://www.thecambrianline.co.uk