I live up in north county so I only make it down to San Diego a few times a month, mostly because of the god awful traffic(which is also an unfortunate part of living in SoCal). But I second Fiesta island, it is amazing! Though unfortunately I can no longer go at least when it's busy because my GSD has turned into a big bully since turning 1.
There's also Balboa park and Seaport village if you just want a nice stroll through some beautiful scenery. Seaport village has a few dog friendly restaurants as well, the pier cafe being my favorite, the Prado at Balboa is dog friendly as well. Both of those places are most excellent socialization spots for puppies as well if you ever get another dog, tons of different types of people and all kinds of things to be exposed to. There's a big dog park at Balboa too if your dog likes that sort of thing.
If you like to hike I'd recommend the Laguna Mountains, some great trails there my favorites being the big Laguna and sunset trail!
Ocean beach is great if not a little seedy but great dog beach and a bunch of dog friendly restaurants. Also there's a lure coursing club that hosts lure coursing events every month in Ocean beach, they also have some agility and nose work you can try out. They will be starting back up again in March, my dog LOVES it. http://www.luratics.com
So many options! I'd also recommend checking out http://www.bringfido.com
,I use it to find a lot of the cool dog friendly stuff.... I don't have kids either so my dogs go with me everywhere they can.
ALSO the San Diego GSD club hosts free training for GSD's every Tuesday in the San Diego zoo parking lot, it's usually held at 6:30pm I think but not sure about right now during 'winter'... Maybe someone else can chime in on that. I try to make it whenever I can!