I am really puzzled by the above advice. Unfortunately, I disagree about staying in Kirchzarten. If I had a car, Kirchzarten would be ok but not if I were relying solely on public transport. Freiburg has the main train station and that makes connections all over easier. If you were in Kirchzarten, you would always have to go through to Freiburg to connect unless you are going somewhere in the other direction. For example, if you were to go to Basel for a day trip, it would take you 1 hr from Kirchzarten and 33 min from Freiburg. I feel that when you are on holiday, time is precious. You want to make the most out of your time in a place.
If I were staying anywhere a week, I usually take an apartment. It gives me more space and the opportunity to not go out to a restaurant for breakfast, lunch and dinner. The food gets so monotonous. You don't have to do major cooking.
Also, Freiburg is a lot bigger than Kirchzarten and offers more to do in the evenings. You can choose from a wider selection of restaurants and cultural activities e.g. jazz concerts etc.
Tip: when in Freiburg, go up to Greiffenegg Schlössle - http://www.greiffenegg.de for lunch or to their beer garden. You'll get a lovely view. Another place with a view is the Schlossbergrestaurant Dattler.
The City Night Line train goes direct from Copenhagen to Freiburg. This is the only train without changes. It leaves at 18:46 every day except for Sat where it leaves at 17:24. This schedule may change but it'll be around these times. It is only possible to buy tickets online 3 months before the departure date. I would suggest that you do it on the first day possible as there are usually specials and you may get a good rate. Usually the later you book, the more expensive.