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.
Whenever I feel uninspired I visit the (now genericly named) Design Museum, formerly known as Kunstindustrimuseet. Sort of the V&A of Copenhagen. An old museum filled with gorgeus fabrics, weird artifacts and a cozy library filled with books about arts & crafts from around the world. If you're still uninspired after a visit here you're not able to. Don't forget to have lunch in the beautiful center garden surrounding by the overgrown buildings, statues and old trees.
Great little chocolate shop that features sweets and cakes with a different take on chocolate. It's part of the Summerbird chain of small chocolate shops, but this one is the "Pure" shop and is dedicated to experiment with flavours and try out new recipes before they are launched in the whole chain. Every month the shop creates a new "flødebolle"(cream bun) based on the time of year and what's available from nature in a limited batch. I'm hooked and need to go there at least once a month.