Hi. I am a native English speaker who lived in Denmark for a few years. I only moved back to the USA some months ago. I lived in Nordylland, so I am pretty sure that is the accent I speak with. Supposedly, this accent can be a bit harder to understand than "Copenhagen Danish," but I don't really know
The Queen also speaks very clear Danish, and you can listen to her New Year's speeches (nytårstaler) on YouTube and get the transcripts on the Kongehuset web site:http://kongehuset.dk/monarkiet-i-danmar ... ytarstaler
She also narrated a H.C. Andersen films that is available on YouTube (Snedronningen), and it sticks closely to the written tale so it is relatively easy to follow.
ETA: Oops, I sort of accidentally skipped over the fact that you prefer books. Well, I also have a book called Gud Bevare Danmark
by Kristian Jessen & Jeppe Facius with the Queen's speeches and analysis of them.