Ordrupgaard is a beautiful museum with lots of interesting exhibitions. Right next to the museum Finn jul's house is located, a famous danish designer and architect. 

Great coffee and breakfast - and a very nice soundsystem.

For wine purchasing a good place is Rosforth & Rosforth. Even better is the location, under the knippelsbro bridge, very hidden. Also nice for their professionally pleasant service and knowledge. And also for the interior.

Best shawarma in Copenhagen. Open until 5am in weekends

Nice place in summer for drinks and food. Close to the water as I prefer it. Music and nice dancing if the company is right.