Go for a coffee break on the hidden terrace of restaurant L'Alsace in Copenhagen. L'Alsace is at the end of an alley, tucked between old houses, a fountain and some greenery. The courtyard is extra romantic during summer, when you can sit outside and enjoy the shade of the neighboring half-timbered houses.
By the way, the cuisine is great, too! A combination of French and Austrian cuisine, yumm!