One other suggestion for the Peak District.
The area it covers is huge so you may be better concentrating on the nearest side to which you live (or which you are going to approach the Peak District).
In you live Manchester or North West go to the NW or West part of the Peak District (Glossop or Buxton etc)
In you live Sheffield or North East go to NE or East side of Peak District.
If you live south of Peak District go to Matlock or Bakewell.
No point in having to travel right across the Peak District if you are only going for a weekend.
In understand the Northern part of the Peak District is hillier than the South.
Here is the National Park web site
http://www.peakdistrict.gov.uk/
Here is the Peak District tourist site
http://www.visitpeakdistrict.com/