Short break in Peak District or Lake District-Recommendation

[michaelw3628]

I'm considering a short break away for between 3-4 days and considering either the Peak or Lake district.

Any suggestions of places to go/ see and also roads to drive and sights to see.
If anyone has any maps and routes they have done previously including ideal places to stay on a budget. Looking at going at the end of May.
Thanks in advance.