It is about a 15-20min. drive.
The trouble with August is that the beach is busy so you'd have to find parking a few blocks away and walk.
You could continue driving north into our La Jolla neighborhood where you could walk in Torrey Pines State Reserve and/or watch the hang gliders take off from the cliffs at the Torrey Pines Gliderport.
While you are at the zoo you might also enjoy walking in Balboa Park(where zoo is located) . In Aug. the zoo is open until 9PM so you can take a break and get your hand stamped and go out into the park and go back to the zoo later.
In addition to small museums of all sorts there are gardens(inc. desert/rose),artisan shops,interesting architectures,street performers and on Sundays free organ concerts and international entertainment.
You will have plenty for your 3 days and might have to come back to "do it all".