In reply to Gile5:
Just google "Sheffield Journey Planner" and tell it where you want to go, it does everything for you.
As a non driver myself I know from experience that Stanage is a ball-ache to get to. We did bus to Hathersage then walked up but that is one hell of a hill, worth it when you get there though.
The easiest for public transport from Sheffield are Burbage (bus to fox house), Froggatt (bus to froggatt and walk up), train to grindleford for Yarncliff, Millstone or Lawrencefield (or bus to surprise view) & bus to Stoney Middleton for Stoney & Horseshoe Quarry (walk to Horseshoe from Stoney not much fun but I've done it a few times and it's doable).
Hope that help.
Chris