Since it’s harvest time, I decided to look up some places around the country to pick or harvest fruit, mainly berries, plums and apples. Here is a useful website if you want to venture out and “pluk selv” / pick yourself!
Here is a site dedicated to places where you can pick Danish strawberries: http://www.danskejordbaer.dk/
A secret source (a family friend), tipped me off on where to find blackberries, my all-time favorite berry, in the wild. The area in the southern part of Zealand, “Knudshoved Odde” should have loads of blackberries right now but for those closer to Copenhagen, there should be some in Amager fælled from Bryggebroen to ITU (the Technical University) where the path comes out of the fælled at the roundabout, Ørestad Boulevard / Tom Kristensensvej.
Also, if you’re interested in visiting an organic farm, visit Økologisk landsforening to find a shop or farm that you can visit and go right to the source for your fruit and veg. We visited one based on the honor system. You just put your money in a box and take what you wish.
Many also have gårdbutikker, or “farm shops”. Here you can find a list of gårdbutikker around Denmark.