If you are driving, I think the quickest way to see the castles in the Cardiff area is to go to Caerphilly Castle first. You can see this from the outside for free so you might not consider actually paying to go inside. Then go to Castell Coch - which is best seen in the morning when the sun is on the main entrance. Again, you can see this one for free from the outside. However, I think it is well worth paying to go inside & see the ornate rooms.
Then, I would drive to junction 32 of the nearby M4 and head west to come off at the next junction (33) & take A4232 for just over 1 mile - look out for brown signs for St.Fagans Castle & Museum. Note: it is a very sharp turn from the slip road off the expressway into the drive. You will need about 2 hours to see St.Fagans Castle & grounds. The place is undergoing a refurbishment so if you want lunch, walk out through the village gate - turn left & go to the Plymouth Arms - entrance up side & round the back. You can then simply return through the gate (for free). On leaving St.Fagans, return to expressway and follow it for about 4 miles to Cardiff Bay.
PS> Don't forget Cardiff Castle. www.cardiffcastle.com
Tintern Abbey is a ruin in the beautiful Wye Valley. Again, you can see this for free without actually paying to go inside. (Pay if you wish).