Sønderborg is a city where you'll meet a lot of German speaking people, both tourists and citizens. I don't particularly like the south, but if I had to choose a place it would be there.
Vejle would be my recommendation if none of that is important to you. Great looking city, not too big nor too expensive, excellent night-life and overall a great place to live. If I didn't have my job in Copenhagen I would move there.
Aalborg is another great city to live in, but I guess it would be too big for your standards.