Ally,
Getting a tee-time/tee-times should be no problem at all, this goes for all of Denmark. (And Sweden). I'm farly sure it's walking only, don't know whether thats an issue for anyone in your group?
I live in Copenhagen and if you decide to play there i will make it work if I'm at home. You should consider asking the club whether the Superintendent (his title is Chief Greenkeeper, as everywhere here), Martin Nilsson, would have time for a 15min chat. We have some very tough environmental regulation here, maybe the toughest in the world ( i don't know, but wouldn't be surprised) and i believe that Martin is considered as one of the top-guys within his field. I've been told that what they do here is quite special/oldschool, but again i'm not an expert.
I've met him cassually a couple of times when playing there and he seems very eager to tell about it if he has the time.
Also, if you need any other advice, Hotels, restaurant, golf etc. don't hessitate to ask.