Veterans Memorial Park.
This park is located just across the bay in easy walking distance. There you will find an oasis with a vriaty of wildlife. You will most likely encounter squirrels and larger and more exciting animals. Very comon animals in the park is also racoons, turtles and even manatees.
If you want to burn some calories in the morning before the sun comes around for real, then you should bring your running shoes. Its a great morning run!