Zoo Miami here.
This Saturday September 29th, you can get free admission to Zoo Miami. You have to go to the Smithsonian Museum Day website to download your tickets. You can get 2 tickets per email address.Once you get to the ticket form, simply look under FL, and then scroll to the last FL museum...Zoo Miami.
On a personal note, I can highly recommend getting to the Zoo as early as possible, as it can get hot in the Zoo here in South Florida. Renting a family big will also be a splurge well worth it, because Zoo Miami is enormous, and from personal experience I can say that walking the entire zoo is tough for both young and old.