I Lived In Denmark for 11 years , All of Martins Picks In Sweden are great , and there are many more , In Denmark near the Capital you should go to Royal Copenhagen (DyreHaven) which is very special , The Scandinavian is nice if you can get on , Rungsted is fantastic, over on The mainland , Aalborg , Holsterbro, Fano, and Esbjerg are all worth a look as is Silkeborg.
On the Islands Falster is really Nice , St Knuds is nice on Fyn. There are also a lot of New RTJ courses and even a New Golden Bear course on its way so plenty of choice ,
Have a nice trip and hope this Helps