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.
My favorite gallery in Copenhagen, located in the meatpacking area... its great for spotting up and coming talents but also established artists from around the world.
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.
Nestled just north of the city, Dyrehaven is a vast, surreal landscape of meadows, castles, and gnarled fairy-tale like forests — Inhabited by a seemingly infinite population of wild deer. Lovely for runs, strolls, woodland adventures, and the like.