This bridge leads from the center to Christianshavn and Amager. Christianshavn is a really sweet and old area, with a canal with lots of boats, nice restaurants and cafes. Right next to Christianshavn is the Freetown Christiania.
Assistens Cemetery is one of the only cemeteries in the center of Copenhagen and beside from being a beautiful calm place to hang out, sunbathing and having a picnic, it is the final resting place for many great people through times. H.C Andersen, Søren Kirkegaard, Niels Bohr, Henry Heerup is just a few of them.
In the summertime you can take the Metro directly to the beach. And if you're over the crowded white trash tanning and blanket sex scene, enter the hidden away mens or womens area located in the big wooden beach bathhouse. Here you can lie naked and enjoy the sun on your private parts while reading a novel or surfing your iPad. Expect lots of gays and lesbos which can be a curse or a party depending on who you are as a person.