Another option: base yourself somewhere in Amber Valley, or with access to it. (e.g. Derby, Duffield, Belper, Whatstandwell, Cromford, Matlock Bath, Matlock.)
A railway line runs all along it, and so do frequent buses (up and down A6). Walking is quite different from Edale, of course, not as "rugged", but actually probably harder to navigate.... certainly in Belper/ Shottle area ,for example, where stiles are well maintained, but paths are so seldom walked that line of path is not always evident on ground. Beautiful quiet valley, once you're 10 mins walk away from main towns such as Matlock or Belper.
Certainly plenty to do on rainy days... Belper is a world heritage centre, Derby a medium sized city (and 30/40 minute train ride from Nottingham and Sheffield).
A bonus for me is that pretty good hotel accom is available in Derby at a good rate (as cities go)... I don't "rough it" of an evening nowadays.