Indianapolis bans fire arms in city parks. More problematic is the state law dealing with schools and property being used by schools.
1. In or On School Property.
2. On a school bus
3. In or on property that is being used by a school for a school function
To paraphrase a book on Indiana fire arms law " there is absolutely no case law to determine parameters regarding facilities being used by a school" so unless you feel like being the test case for Indiana law I would suggest discretion is the better part of valor.
The good news is that the zoo pretty safe so is the circle center area downtown. I carry when I am down town, but would not feel it unsafe to take my family to the zoo unarmed. Getting to those areas can be tricky, but once you are there things are OK