Another suggestion starts at Conksbury Bridge, then takes in Alport, Stanton In Peak, Stanton Moor, Birchover (including its 2 excellent pubs
), Robin Hoods Stride, Youlgreave, and the lower reaches of the river Lathkill, in that order. I often incorporate this section into a longer walk in the area, as it has a nice mix of terrains. Some folks may not like the couple of road sections, but in this area they're pretty much unavoidable . . . .
If you want to add on a few very picturesque miles you could always start at the layby in Monyash or the car park in Over Haddon, and include Lathkilldale . . . .