Lets assume that you do your planned journey from Bath to Conwy via Tintern. The AA website tells us that this would be a 200 mile trip taking 4 hours 28 minutes (without stops). http://www.theaa.com/route-planner/index.jsp
So, it is doable. The main problem with their route is Hereford - which can take 20 minutes or so just to get from one side to the other as it lacks a by-pass. (It does contain an ancient cathedral).
The first thing to note is that Chepstow has a Norman Castle. (This is the first Welsh town you reach when crossing the M48 Severn Bridge from England). http://cadw.gov.wales/daysout/chepstow-castle/?lang=en
Then it would be a 20 minute drive up the Wye Valley to Tintern.
This place is between (slight detour) Hereford & Leominster:> http://www.hamptoncourt.org.uk
When progressing up the A49 between Hereford & Shrewsbury, I would definitely take a detour into Ludlow. This is real Ye Olde England and also has a Castle - best seen from the west bank of the river. http://www.ludlow.org.uk
Just north of Ludlow is Stokesay Castle - a fortified Manor House rather than a proper castle.http://www.english-heritage.org.uk/visit/places/stokesay-castle/
Shrewsbury is also worth a look - but you simply would not have time.https://www.visitshrewsbury.co.uk
A detour to the west would have taken you to Welshpool and Powis Castle - Which has lovely gardens:>http://www.nationaltrust.org.uk/powis-castle-and-garden
So, what I am pointing out is that many places of interest lie en-route - or near route. The chances are that you would not have much time to visit such places by doing this journey in 1 day. In fact, ideally, I would take 2 or even 3 days to do such a journey & having detoured to Welshpool to see Powis Castle, would then head west via Dolgellau & Barmouth to take in Harlech Castle on the west coast. So, consider the driving time plus visiting time. Doing it in 1 day means you have to simply keep driving for much of the time.
Check your timings / distances with the AA website. When going from Conwy to Keswick - I would call in at Chester.