The answer to your question is:
1. You should get your divorce in South Carolina, because it will be the only divorce recognized there. The basis for this is the 'UNIFORM DIVORCE RECOGNITION ACT SECTION 20-3-410' (available here: http://www.scstatehouse.gov/code/t20c003.php), the point being that South Carolina does not recognize divorces obtained abroad while the parties where domiciled in South Carolina;
2. Strictly speaking, you could obtain a divorce also in Germany (not Denmark), on the basis that your wife is German. However, for US purposes, it would be unwise, since it would not be recognized.
In the other way, from the US to Europe, a South Carolina divorce would be recognized both in Denmark and in Germany.
I hope my answer was helpful and look forward to your rating, which is essential to my activity.
Cordially, Dr I L Vlad
(please make the distinction from the other site member, Jose M, when rating!)