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. 

This is a lovely place to go if you want to enjoy the beach. It's also beautiful when its not bathing season. Go check out these little beach houses in beautiful colors. Also make sure to go for a walk in the forrest just next to the beach. 

A pretty museum located 30 min north from Copenhagen. It has a stunning sea view and beautiful architecture. Here you can explore many exciting exhibitions. They have a great cafe as well.