For the best danish possible, get yourself to Juno the Bakery right when it opens.
This bakery was founded by Emil Glaser, a former Noma chef, and some of its bakers are on the Swedish national baking team… Let that sink in.
The cardamom buns are "to die for". I recommend spiriting your carbs and coffees away to Faelled parken, the largest park in Copenhagen and very popular. Expect a fast moving queue out the door for their black coffee (only) and pastries, $10.
If lining up for pastry strikes you as utterly stupid, you can instead breakfast at Coffee Collective in the once-dangerous and now gentrified suburb of Jaegers borggade. You'll spend about $15 for a tasty meal paired with a complimentary cup of coffee.
Let yourself loose on Jaegers borggade with its charming coffee shops, cafes, bakeries and independent shops. Look out for Tricotage for clothes, Vanishing Point for craft and design, Ladyfingers for jewellery and Cactus Copenhagen for pottery.