Your backyard is meant to be the family’s oasis. How much of it needs a permit depends on how big, how permanent, and how intensive a project it will be.
A blow up kid’s splash pool does not need a permit.
A swimming pool (above ground or below) will require a permit.
A swing set will most likely not require a permit, though it may.
A full play land will most likely require a permit. Also, you need your HOA’s approval.
When in doubt, your city’s Building Department is happy to answer a question. It is better to ask first than pay fees from skipping the permit process altogether.