I am thinking that many of my readers may have thought of the Stones when they were looking for a place to stay. Well you are some what correct. If you are looking for a place to stay as you wander or cycle in Denmark then there is an App for that, Shelter. The following screenshot indicates the availability of sites through Denmark, yes there are many.
I use this app regularly to locate possible campsites and shelters in Denmark, it is only available in Danish but using the map it is easy to locate yourself and determine where the nearest shelter (or campsite is).
Having located the shelter (or campsite) you can then click on the site and determine what is available.
Here your lack of Danish is not an issue, as it is soon obvious what is available at the campsite, in the case below there is a shelter, a campsite, water (though it may be turned off during winter) you can have a fire but please don’t bring your dog or your horse as it is a national park. (For my Danish readers, yes I am aware of the contradiction in the text, but for all intents and purposes you can erect a tent between the shelters)
So as I stated in my introduction, this app provides a very useful resource if you are looking for free accommodation on your travels around (or through) Denmark. Are there similar apps in your country? Tell us about them, so that fellow travelers can use them as part of their planning.
By the way I have no affiliation with the Shelter App, I am just a user.