The St. John's County Arboretum is part of the Agriculture Center complex. It is maintained by a small staff of dedicated professionals, and some great volunteer master gardeners. The garden isn't all there is, the surrounding area has little ponds, a larger lake, hayfields, and all the birds and other critters you could want.
You may see raptors, from American Kestrels to Cooper's Hawks. Gallinules and Coots like the ponds, Little Blue Herons, Anhingas, and Great Egrets are common.
Just move slowly, and sit a lot. Look in the bushes, not just at the bushes.