Shingle Creek State Park is billed as the northernmost part of the Everglades. When I worked in Orlando 1, I used to like to unwind here, as its pretty empty. Facilities aren't great, but you get a wonderful sense of the cypress trees and what the flora and fauna are like. I can't say I ever saw a lot of wildlife, but the trees themselves are fabulous. I can't say as it would be the highest thing on my "to do list" in Orlando, but its nice.
Beyond that, there are always "Gator Parks" like Gatorland, not too far from Kissimmee. They're tacky, they're not what I would call "wildlife," but if you want to see a gator and a cheap zoo, this is the kind of thing you are looking for.
One word of warning - you might be tempted to drive to the Miami Area in order to hit the Everglades region. Its a long drive. If your time is limited, don't bother.
Lastly, as far as wildlife and zoos go, Disney's Animal Kingdom is actually pretty good. They've got a "safari ride," as well as great "Maharajah Trek" and an amazingly well done bird show. Orlando is mostly strip malls and kitsch. Embrace it, and you may be happier in the long run.
1Full disclosure, I worked for Accenture at Disney World - Hollywood Studios for most of 2011, doing websites. I'd fly in every Monday and out every Friday. I was by no means a Disney-phile when I started, but I came to appreciate the kitsch for what it was.