I had always thought that Conwy was the English castle and Deganwy, the Welsh. What I hadn't realised until now was that it was built by the Anglo-Normans and strengthened by the Welsh, before being razed by the Welsh under the threat of English invasion. A very comprehensive history and walking guide to the area can be found in pdf form here, and makes a fascinating read.
It's a very easy walk up to the base of the two hills that the castle spanned. Access is via a footpath leading from Gannock Park road in Deganwy, where the road loops in a circle. The hills themselves are the hard remains of volcanic plugs, like a miniature version of the hill upon which Edinburgh Castle is built.