La Jolla Shores is a mile long gently sloped sandy beach- on the north end is Scripps pier and the Scripps Institute of Oceanography and to the south near the cliffs is the La Jolla Park Ecological Reserve.
I've swam here with stingrays, seals, dolphins and even came upon a leopard shark- don't worry though, these sharks are docile (unless cornered) but still can make a heart race when you're right next to one in the water!
There are businesses nearby where you can rent scuba and snorkeling gear, kayaks and wetsuits. The Ecological Reserve is a great place to kayak and where you can see leopard sharks, seals, dolphins and the state fish, the giribaldi. Giribaldis are easy to spot since they are bright orange! There is a little tunnel the ocean has carved from the cliffs to kayak through and I recommend kayaking over to Children's Beach where you can check out seals lounging on the beach. Just keep an eye out for swimmers and be sure to stay our of the swimming lane. This area also makes for great snorkeling.
During winter, the ocean covers most of the beach, so spring, fall and summer are the best times to enjoy this location.
Tip- If you're driving here from downtown San Diego, keep in mind that there are only 4 lanes in and out of La Jolla. Traffic into the area in the morning is worse, and leaving out in the evening is tough. The best time to drive here is either in the morning before or after rush hour (7-9am) and leave after or before evening rush hour (4-6pm)