Sadly the geology of Derbyshire (& Staffordshire) doesn’t lend itself too well to a walking + caving challenge.
Would recommend Nettle, Maskhill and Oxlow. Nice because they’re all so close.
Orders of magnitude easier than 3 Peaks, 3 Pots; in a team I’d say it’s just a good day caving, solo it’s moderately hard with rope logistics being the hardest bit really. Hope you like hauling.
More challenging options exist, e.g. like JH, Rowter (extensions) and Winnats Head (up and down, to make sure you get the full enjoyment of taking the rope through the boulder choke).
Similar to mountaineering just how challenging it is depends substantially on your approach/ ethics. Pre-rigged: Fairly easy verging on enjoyable. Rig & de-rig: bit more engaging. Solo & rig everything yourself: full experience you might regret.
Fair warning: JH is naff solo (cartgate + multiple heavy tackle sacks), the Winnats chokes are a bit of a pain but not as bad (less rope), only ever done Rowter pre-rigged so couldn’t say.
Spoiler: pdf contains details exactly how I sorted ropes for Nettle, Maskhill & Oxlow, don’t read if you want to do the logic puzzle yourself. Rope lengths only work for solo & 0 slack.