Between colony gardens in Amager lies one of my favourite local spots: Baghaven. Good food and cosiness is in the forefront. Various events with and without music gather people on the square at Diamantgangen 75. A very local experience. Great for families, children, young and old.
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.