Data from the US National Park Service.
National Park Service, US API is a free Government API that requires apiKey authentication, is served over HTTPS and supports CORS, so it can be called from the browser.
Developer Resources
Details from nps.gov.

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Yes. The National Park Service, US API is listed in the Government category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
Yes. The National Park Service, US API uses apiKey authentication, so you need to register for credentials before making requests.
Yes. The National Park Service, US API supports CORS, so front-end JavaScript can call it directly.
Yes. The National Park Service, US API is served over HTTPS, so it's safe to use in production.