Britt Gardens were originally created by photographer Peter Britt, whose home was on the 4.5 acre hillside parcel. Manicured foot trails remaink, but now the park is primarily devoted to the summer festival of music, which are fully described by the web link below.
Jacksonville has several parks oriented toward local residents that tourists may also use. Just below the cemetary is a skateboard park that's not overly crowded, but is well designed for the purpose. On the southeast side of town is a public park with playground equipment and picnic tables for families and groups.
Deer are treated very well in Jacksonville. Hunters would consider them treated too well as they are plentiful even in town. I don't recommend trying to pet one, but they sure are cute to watch. Unfortunately, the excess population of deer isn't due so much to a lack of hunters, but a low population of natural predator species in the area, such as the cougar or mountain lion.