What Supreme Court tests apply to a city park-gathering ordinance?

[MiaUD]

I'm a journalist researching a story about a recent local ordinance that restricts public gatherings in certain parks, which some civil liberties groups argue infringes on constitutional rights to free speech and assembly. The city council claims the restrictions are a reasonable time, place, and manner regulation for public safety. I'm trying to understand the legal precedent for such limitations, particularly how courts have balanced First Amendment protections with municipal authority to manage public spaces. What are the key Supreme Court cases or legal tests that would likely be applied if this ordinance were challenged, and how have similar restrictions fared in other jurisdictions?