Slottskogen is a large park with free roaming and captive animals. Most of them are local animals like moose, roe deer and seals, but there are also flamingoes, penguins (for Linux lovers!) and others. No entrance fee.
It's also splendid for barbeques, playing soccer and other outdoorsie activities!
You take the tram to Linnéplatsen or Botaniska Trädgården to get there.
Gosh! I have never seen a moose. I just have to go: