In Old San Juan, going from the cruise ships by the Sheraton to the west until reaching the entrance to the bay, then right along the cliff until reentering the town, and from there left until you get to El Morro is a nice walk and one that on a good day can give some birds including Caribbean specialties. For the one day with a car, I would likely go to El Yunque, you probably do not really have time for the other good locations.
Niels