Felix Paturi in his book Prehistoric Heritage says that "The are still 24,000 stone 'dolmen' preserved in Denmark today as well as huge barrows, stone circles and other prehistoric monuments"
24,000 does seem an awful lot of monuments, unfortunately he doesn't provide a gazetteer.
If his figure of 24,000 isn't a typo then I guess you'll be tripping over the buggers.

The Danes call their dolmen 'dysser' and the oldest ones are to be found on Zealand. There's a megalithic cemetary at Tustrup in the county of Randers in East Jutland that's been restored, I've a couple of pictures - it looks beautiful.

Have a good trip