If based in Castleton and you don't want to travel far, then you still have loads of choices of wonderful locations to concentrate on. Despite the name Peak District, the highest peak is 631m above sea level (Crowden Head on Kinder) so you will not see big mountains, but nonetheless there are some great hills!
My top five suggestions:
1. The Great Ridge. From Mam Tor which rises above Castleton along the ridge to Lose Hill. Some great views from here across to Kinder, Win Hill, etc.
2. Kinder Scout. This is at its most dramatic in what little snow we get or when it's freezing - Kinder Downfall frozen is quite a picture, although in May it will be flowing well. Take a compass though and follow the footpaths or you'll get lost in the peat on the top. Brilliant walks and views.
3. The gritstone edges. There is about 30 miles of millstone grit that has risen about the Derbyshire limestone to give some fairly dramatic escarpments between Howden in the north all the way to Chatsworth and Beeley in the east of the area. Favourites are Derwent Edge (above the reservoirs - Ladybower, Derwent, Howden), Stanage Edge, Froggatt Edge and Curbar Edge (the last two join almost seamlessly). Bamford Edge is also marvellous - not for its own geology, although its certainly not boring, but I think provides the best views in Derbyshire. These edges are well positioned for sun setting - they are lit up beautifully and simply glow as the sun drops. In shadow at sunrise though!
4. Padley Gorge. You must see this as it is an absolute gem, but go mid-week and preferably when it's bright but cloudy. This is a beautiful wooded gorge that runs down from the Longshaw Estate to Grindleford.
5. Lathkill Dale is another gem and quite beautiful. Quite a contrast from much of the millstone grit of the Dark Peak above as it runs through a limestone gorge (part of the White Peak area).
I cover a lot of the above on my website but also check others in the area including Fran Halsall, Karen Frenkel, Dave Butcher.
One of the great things about the Peak District is that it is not huge and you can cover quite a lot, but the downside is there's far too much to see! If you want to see Derbyshire customs May isn't the best time - well dressings start in May and really get going a little later (see www.welldressing.com
) Also get to see Haddon Hall and Chatsworth House (and Gardens) if you like stately homes.
Let me know if you want further picks or suggestions,