Hi Rob,
Do you know if you're going somewhere near Copenhagen (Which is located on Zealand) ? - Billund is located in the middle of Jutland a bit from Copenhagen (3-4 hour drive), Billunds main attraction is LEGO land, which is worth a visit, especially if you have kids.
I'm a Dane, and thus living in Denmark, 15 minutes south of Copenhagen. I'm allways ready for a beer or two. Let me know your traveling plan, perhaps i can recommend a thing or two to see while you are in our wonderful little country.
All the best,
Kaare