1 night in Cardiff is not really enough time to see all 4 castles within 7 miles of the centre:= Cardiff, *Castell Coch, *Caerphilly & St.Fagans Castle - which has gardens and the Museum of Welsh Life - which takes at least 2 hours to see - and that is walking around the extensive site quickly. I would not choose a city centre hotel due to parking issues. You may also wish to allow time to visit the waterfront in Cardiff:> http://www.mermaidquay.co.uk
- It may be possible to make quick detours to these castles prior to starting your drive to Aberystwyth - assuming you use the A470 route via central Wales.
It takes just over an hour to drive from Bath to Cardiff but the M4 frequently jams up at Newport - especially from about 7.30am to 9am & 3.30pm to 6.30pm on weekdays.
When you drive from Cardiff to Aberystwyth - I would take the A470 going N from Cardiff via Builth Wells - where you will find a cafe just over the river bridge with toilets (which are few and far between). From Llangurig, take the A44 to Aberystwyth. I think that the A470/A44 route is better than going via west Wales. If using the A470 route, you may like make a short detour at the village of Libanus to the Brecon Beacons National Park Mountain Centre. Near Rhayader, is a farm that has wild Red Kites flying in to feed:>
The Folly Farm place mentioned above - is well off your route - that is assuming that you take a westerly route.