Below is a map and list of the more "local" recommendation:
Quark Nature Center and The Troll Trine
Avedøre Tværvej 56, 2650 Hvidovre
The Circus Museum
Hovedporten 6, 2650 Hvidovre
Website: https://cirkusmuseet.dk/en/velkommen-english/
Brøndby Habour and Beach
You can cycle via the path system all the way down to the harbour and the beach. It's about. 2.5 km down there. The bathing water is shallow, clear and child-friendly. At the harbor you'll find a very good restaurant (Albatrossen) and a grill bar and playground.
Vestvolden
We live right next to Copenhagen's old fortifications, which were built at the end of the 1800's. It is a very beautiful place with fantastic nature mixed with the old fortification buildings. We love to come down there and walk, run or cycle along the embankment.
When leaving the house turn right og then left at the path towards Vestvolden. Today, the 14.2 km long Vestvold stretches from Utterslev Mose through Copenhagen, Rødovre, Brøndby and Hvidovre municipalities to the salt marshes in Avedøre. The rampart is protected in its entirety as both a historical monument and for its biological and natural values, and it functions as an integral part of Greater Copenhagen's recreational and green areas.
Vestvolden is also a popular cycle route, which is used every day by many Copenhageners.
ARKEN Museum of Contemporary Art
Skovvej 100, 2635 Ishøj
The museum is an experience for both adults and children. They often offer children's activities based on art.
Website: https://www.arken.dk/en
Ishøj Swimming Hall
Ishøj Store Torv 14, 2635 Ishøj
A good and child-friendly swimming pool with many different pools. But remember to bring your own swimming fins or swimming belt.
Hvidovre Friluftsbad: https://friluftsbadet.hvidovre.dk
Nice outdoor pool however the ocean is better :)
Ishøj Dyrepark
Nice place for a walk, there are playgrounds and animals (scottisch highland cows, goats, deer, etc.)
Go to a Football game with Brøndby IF (SuperLiga) , Hvidovre IF (1. division) or FCK (SuperLiga), check their schedule: