Helsinki provides us with two nice places to watch animals: Haltiala farm and Korkeasaari Zoo. At least 3 years old kids were thrilled about both of the places.
Horses, cows, lambs, pigs, chickens, roosters and an ugly gobbler - those are the animals of Haltiala farm (sorry, they don't have English website). Haltiala farm is owned and maintained by Helsinki City. It's located in Northern Helsinki, near Jumbo shopping center. The public transportation is not impossible: bus 650 takes you to few hundred meters from the farm.
In the summer time the animals are out around the clock. The ice cream kiosk and restaurant have more limited opening hours. No entry fee. The farm is growing flowers and peas - and the citizen can pick them for free (whenever they're ready for harvesting). Isn't that nice?
Helsinki Zoo is located on an island, Korkeasaari. You can get there by metro (+ couple of kilometers walking), bus or boat. If the weather is good, I recommend the boat - but take it from Hakaniemi instead of Kauppatori. And they sell tickets in the boat too, so you don't need to queue and miss the boat because of pre-sold tickets.
There is quite a variety of animals in Korkeasaari. Not the farm animals, though. And no elephants, polar bears nor giraffes either. But there are lazy lions, a tiger, snow leopards, lynx, bears, baboons, all kinds of deers, camel, owls, otters and small apes and parrots. On a summer day you should be prepared to queue everywhere. If you're not in a hurry, postpone your zoo visit to September - then the animals are much more active.