Denmark is made of many different towns and each one is different because it has a variety of languages and origins but no matter where you visit throughout the nation, there is plenty of things to do and I would strongly recommend visiting each city and region if possible because whilst the overall culture is the same, each has something different to do.
I would investigate each town carefully because the locals will behave differently and it is important to know if you will need to rely on a dictionary to help out because not all places throughout Denmark speak English.
There are many cities throughout the Danish countryside that offer a variety of sights from long beaches to historic castles that will offer something suitable for everyone. You will have something to enjoy on a daily basis and with the rolling hills and beautiful oceans, there are many days that will make an excellent family holiday.
Each part of Denmark has a magical touch to a trip and it will be a very enjoyable trip because overall, there are many places to relish and the countryside and history is completely breathtaking so you may be surprised what this Nordic community has to offer.