Whilst Kantara is not quite as precipitous as St Hilarion, wandering around it does mean walking on exposed rock as well as stones.
These are slippery, and even more so when they are damp from dew or wet from rain. Wear shoes with a good grip. It's not a place for flip-flops (thongs).
Equally, don't expect EU health and safety precautions. The site is fenced and has hand rails in parts, but there are many areas where it would be easy to fall. Watch your children closely.......it's not a place to let them explore alone, or to run free.