The Lakes in Copenhagen is often referred to as the lungs of Copenhagen. It is a row of five artificial lakes surrounding the inner city. They span the intire city from Vesterbro, through Nørrebro to Østerbro. Along the shores is a pedestrian path dotted with benches. If you go here, you will right in the middle of the front yard of Copenhagen, where the inhabitants walk their dogs, go for runs and meet for walk and talks. Join them and buy your to-go coffee in one of the coffe shops along the way.
If you are not the outdoorsy type there are many opportunities for a more civilised cup of coffee, a bear or a meal in one the the lakeshore restaurants and cafes.
If you want to go out on the water you can rent a boat. There is even the option to rent a swan boat – good for selfies.