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.
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.
Copenhagen Meetpacking district is a good place to go out for a beer. Duing the summer the hole place is packed with young people. There is several bars, galleries and restaurants in the area.