Years ago when I lived in the suburbs I would put out bird feeders and plant flowers that would attract birds and butterflies. Move forward 10 years and that backyard was now more rural and had increased to almost 3 acres. Wildlife now included owls, jackrabbits, squirrels, barn swallows, snakes and hawks. Mice and rats were in the hay barn and happily kept in check by the barn cats. The next 8 years was low level wildlife and attracting them was no longer an issue since they just showed up. We then moved to a forested rural homestead where now we see deer in the backyard as well as the occasional elk wandering in a neighbors large open field. It has now become more of a matter of learning to live with the wildlife.
As we have moved further and further away from populated areas I now find that maybe some stories of unusal animal sightings might be more real then people are led to believe. I love reading books about such sightings and one that I enjoy is Florida's Unexpected Wildlife: Exotic Species, Living Fossils, and Mythical Beasts in the Sunshine State. It was on sale one year during one of my lazy, just want to curl up with a good book periods.
I don't live in Florida but I have visited the state when I was younger. I remember seeing wild pigs next to the highway rooting around for food as well as 'gators crossing the roads too. I would imagine by now they have some non-native species running amok in the state from escapees or illegal smuggling. That alone would account for some unusual sightings.
Where ever you live I am sure that if you see an unusual animal or bird you would want to document it. Carry a small camera with you or a phone that takes photos. At least you'll have proof of your sighting and not just get strange looks when you tell your tale.