Snowdonia is too far. It's 4 hours to get there from South Wales, which is too much when you only have 3 days and wish to visit the South.
As for staying in a "castle", if you're looking for something with turrets, dungeons and jesters I think you're going to be disappointed. If you're looking for a country house which is not too expensive you could try this one
http://www.crosswayshouse.co.uk/index.php
otherwise there is a youth hostel in St.Briavels castle in the Wye valley, which is a genuine castle, but a "no-frills" accomodation option
yha.org.uk/find-accommodation/…index.aspx
Other country house hotels tend to be on the expensive side.
You could try an old coaching inn instead, which is the more typical place to stay. The Bear at Crickhowell is v.good, as is the 3 Salmons in Usk.
If you want interesting castles - cardiff castle and carreg cennen are v.different but each are spectacular for different reasons.
For mountains - stick to the Brecon Beacons
For coast - Rhosili in the Gower or (a good bit further west) - Pembrokeshire, around St.Davids or around Tenby.
Think about a trip up the Wye valley and Forest of Dean
Big Pit is excellent, as is the St.Fagans Museum of Welsh Life.
Around Bristol and Bath there is also Wells and Glastonbury, Lacock Abbey, and neither Stonehenge nor Avebury are too far away