Balboa Park is right next to the zoo. I'm not sure of all the museums' hours, however, but it's just a nice place to walk around. Do a little research, if you're interested, because there might be some kind of event going when you're here. It has wonderful museums, great architecture, and beautiful gardens.
The new ballpark area downtown (and close to the zoo) is nice--and there's a walking path that goes along the bay by the convention center and Seaport Village, which also gives you nice views of Coronado Island, the bridge, and Navy ships.
The USS Midway aircraft carrier is now a museum--downtown San Diego Navy Pier.
For a smaller, older ship, there's the Star of India/Maritime Museum.
The Hotel Del is very nice too, and it's on a nice beach. Have a drink out on the deck above the pool and watch the sunset!
Those are just a few of the things to do that are near the zoo. There are tons of things to do--big and small--depending on your time and your interests! I actually found the following link on this site, and you might find helpful (I refer to it every so often, even though I've lived here 15 years!):
http://www.localwally.com/index.html.
Have a fun trip!
