As the summer is my favorite time of the year and that the beach is just 15 min bikeride away, I recommend Amager strand. Full of people usually though, but even so it gives a bit of an exotic touch to such a scandinavian city with the sea and the bright sand in the hot summer days.
Copenhagens bikelanes is all around the city. Its one of the best cities in the world to get around on bikes, there is even free bike servicestations around town:)