If you have mobility problems, you will find seeing the interiors of most castles difficult. However, it is well worth looking at the outside of the Castles (for free). At Castle Coch (on a hillside in north Cardiff), the driveway is steep - don’t go into the first parking area you see but stay on the driveway and go right up to the castle. You will see a parking area backing onto a forest - that is the best place to park for those with mobility issues.
Just W iof Cardiff is >https://www.nationaltrust.org.uk/dyffryn-gardens
The National Trust may be able to lend you an electric scooter - or drive you around.
Try not to miss this place on the western edge of Cardiff. Entry is free - just pay about £5 for parking. The place is really in 2 sections. The car park is by the western half - which is relatively easy to walk around - to see buildings of architectural significance from all over Wales. A tunnel connects with the eastern half - which has gardens and a Castle - really a manor house from the 1500’s. A deep valley with ponds separates the Castle & gardens from the rest of the estate. For those with mobility issues - take the road train.
Cardiff city centre is flat and mainly traffic free - so may to get around. It is relatively compact. You may also like to visit the Bay Area - 1 mile S of the city centre. http://www.visitcardiff.com/travel-trade/cardiff-bay/
The A470 from Conwy to Cardiff is very scenic. However, the towns are not up to much. You might like to divert into Llanidloes - instead of using the bypass - as it has a lovely old Market Hall in the middle. (Beware of road humps).
The A470 has few toilet facilities. You will find a public toilet in Dolgellau - which has interesting buildings made out of huge blocks of stone. The ‘Little Chef’ in Builth Wells is also a handy place to stop for a coffee & pee. (This is about 1 hour 40 minutes from Cardiff).
The Theatre by the Canal in Brecon has a disabled toilet with easy parking outside. (Around 1 hour from Cardiff).
The Brecon Beacons Mountain Centre - about 2 miles off the A470 at Libanus - has a cafe and toilets.