Augustendals 4H farm is a great option for families travelling with kids. It is an international youth organisation and the Hs stand for head, heart, hand and health.
Whenever I have had visitors who bring their kids, Augustendals 4H farm has been a big hit. The organisation is run by volunteers and their farm has horses, goats, cats, rabbits and hens. If one wants to visit the stables, guided tours are offered for groups (at a price) but the animals are out during daytime (daily between 8:00 and 16:30) and can be admired and petted without making any reservations or paying fees during that time. One needs to bear in mind that it is not allowed to feed the animals. Augustendals 4H farm offers different courses about handling animals and in the summer there is a café that is open from 10:00 to 15:30 which serves homemade buns, coffee, tea and more.
The setting is quite beautiful, next to Huvudsta Castle and the Lake of Ulvsunda. Horse carriage rides in this tranquil and beautiful area can be booked in advance. The current price is 600 SEK for 4 adults and 4 children, and the ride lasts for 30-40 minutes. There is a playground next to the farm and at the nearby beach there is a variety of wild ducks and swans.
It is easy to get there; take the subway to Västra skogen (blue line 6 minutes heading north from the Central station) and walk towards the water for about 10 minutes.