I agree with Skiingfast, the Pacific Beach/Mission Beach area is probably the most centrally located for what you want to do. And those two beaches are connected. However, if you want to go to those beaches, I recommend going to South Mission, south of Belmont Park/rollercoaster, as it is MUCH less crowded. Have breakfast at The Mission restaurant on Mission Blvd. The zoo is a short drive, downtown is 5 minutes down the freeway, La Jolla is just north, Sea World is literally right there. Lot's of choices.
BUT, I personally recommend going to Coronado to go to the beach. I live in San Diego and Coronado is my absolute favorite area of San Diego and has the most beautiful beach (the Travel Channel's #1 California beach!). It is HUGE and clean, the Hotel Del Coronado is right there and is nice to walk to - explore the shops downstairs, get an ice cream, or sit at the outside bar and have a drink while enjoying the view. The main street, Orange Avenue, has some fun shops and restaurants - there is an awesome candy shop, McP's is San Diego's only authentic Irish Pub, Miguel's Cocina is a great Mexican restaurant tucked in down a little "alley" across the street from the Hotel Del. If you're looking for a more upscale meal, The Boathouse is good.
San Diego is a great city. Have fun!