I believe you are talking about the common buckeye butterfly, Junonia coenia. The large eye spots you saw were developed to help the butterfly scare away potential predators. The common buckeye is found all over Southern US and into Mexico. In Florida, it can be found in all 67 counties. From the northern parts of the United States, the common buckeye butterfly will migrate in the late summer and early fall to spend the winter in warmer areas of the South. Its habitat is most any open park areas, but it visits landscapes with plenty of nectar and larvae plantings too.
The common buckeye produces multiple generations each year. Adults may be found in all months of the year throughout much of Florida. Adults have a distinctive flight pattern and will flit away if humans get too close. I took the attached photo while hunting for pollinator plants at a local plant nursery. You will notice the edges of the wing in the photo are damaged, so this common buckeye butterfly has been around a while. Both sexes (particularly males) perch on low vegetation or bare earth. Females lay the small green eggs singly on leaves of the host plant.
It is important to have plants in the landscape for the caterpillars of our butterflies. Yes, it means the caterpillars will eat the leaves. A few good choices for the common buckeye caterpillar are: plantain and toadflax (most people consider these two as weeds) but the toad flax is quite delicate and lovely. You might consider planting our native twin flower, which is also a good larval plant. The adults will feed on most any flowering plant providing nectar. For more complete information on the butterfly, look over the University of Florida publication titled: “Common Buckeye, Junonia coenia” by Jaret Daniels: https://edis.ifas.ufl.edu/in801