In reply to tnj:
Miller's Dale would be Monsal head and down to Cressbrook
Lathkill Dale would be Monyash or Alport
However although both are interesting I wouldn't describe them as gorge scrambles as paths are reasonable throughout.
Slightly better for that might be scrambling up the Devil's Arse at Castleton, no river though or the river passage round Lovers leap at Dove dale. To be honest they aren't really that sort of gorges.
Chee dale is another possibility