I love this little garden for walks... its less busy than Frederiksberg Gardens (right next to it) and Ive been walking with the stroller here endless amount of times
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.
Ordrupgaard is a beautiful museum with lots of interesting exhibitions. Right next to the museum Finn jul's house is located, a famous danish designer and architect.