If you're really into animals you may want to do one day at the Zoo and one day at the Safari Park (Owned and operated by the zoo. It's a more immersive experience than the zoo and rather awesome in its own right).
Heading up to La Jolla for a day and doing a kayak tour of the cove (with or without whale watching), checking out Children's Pool (home to dozens of Harbor seals year-round!), Mt Soledad, and the surfing beaches is also an option.
If you're not renting a car, I'd recommend staying in a hotel very close to Balboa Park, going to the zoo (which is IN Balboa Park) one day and just exploring the rest of the park the next day (there are a TON of awesome museums in the park and lots of outdoor activities to be involved in as well). You can spend an entire day just exploring the park easily and this will make it so you don't have to rent transportation if you don't want to.