Just seeing this post now, so you may already be in S.D. Of course the iconic San Diego Zoo; Definitely drive to Coronado, park on the street and go hang out at the famous Hotel Del Coronado. You can pack up some beach gear, change in the hotel’s public bathroom, and rent beach umbrellas for a nominal price. Afterward, go to the hotel’s outdoor restaurant and have lunch, snack, dinner, drink, etc. Stay long enough for the fabulous sunset. It’s an amazing hotel full of history. The movie “Some Like it Hot” was filmed there.
Get in the car and drive to LaJolla. It’s beautiful. My favorite beach is in DelMar, where there are also great restaurants. Also, Torrey Pines is great. If you’re into hang gliding, that’s the place to go. While you’re near LaJolla, check out the race track. It’s super fun and you don’t have to bet if you don’t want to. A great sushi restaurant is Riki Sushi in North Park.
Another great day trip is Scripps Aquarium near LaJolla. The views are great.
Enjoy your trip!
Oh, sorry, I obviously didn’t read your post carefully enough, as I missed the “no car” portion. If you have a driver’s license, rental cars are cheap and definitely worth it so you can see more places, like what I suggested above.