Contrary to what you might have heard from misinformed media like the BBC, child care in Denmark is anything but free - you can expect to pay 1500kr per month or more per child. However, it is comprehensive and børnehave (nursery for age 3 to 6) is an impressive facility which our kids really love going to and have made many friends from. There are good and bad though and since they're all the same price in the region you live in, you want to find the best one with better kids, parents and motivated staff who enjoy looking after the children.
Before the age of 3 you can use the state child-minding system whereby a child-minder looks after your child and probably 4 or 5 others in their home. As an outsider who can comment freely on the system I am not impressed because if you take a day off from work you'll often see these childminders dragging the kids around town against their will while they natter with each other and do their shopping. Statistics show that an awful lot of these childminders also smoke, and some deem it acceptable to "smoke out of the window" as enough to protect the health of the children. I apologise if you are a good childminder and you're reading this, but this my personal experience and that of many Danes with children I speak to.
As to children of school age (6 and upwards), I have a tip for you that we only discovered some 6 months after our daughter started school. We were unimpressed with the facilities and then found that for 500kr a month we could send our children to a private school. Prices may vary but I doubt they can vary that much. This must be one of Denmark's least publicised bargains since your children are getting a level of education that costs £1000s in other countries. Now I'm no snob and just had a British comprehensive education myself, but you could tell the difference immediately you walked through the door and met happy, motivated teachers, so of course I want what's best for my own children. Apparently the state pays the same towards your child's schooling as it would have done at the state school. I strongly recommend you find your nearest one, if this is relevant. You will surprised to
learn that in this socialist land over 10% of danish children attend private school. Some men are indeed more equal than others...