If you find yourself in the vicinity of Santa Cruz, CA and are looking for a nice beach to spend an afternoon on, I'd highly recommend visiting National Bridges State Park. It's only about a 10 minute drive from the beach boardwalk, so there is no excuse for not visiting it. As with all California state parks, you have to pay for parking if you park right in the state park's parking lot. Fortunately for you, there is free street parking a 2 minute walk from the pay-for-parking parking lot.
Although the portion of the beach that meets the water isn't as long as some of the other beaches in the area, it has a relatively deep sandy beach area for your recreational needs -- there were a bunch of people playing soccer and frisbee... and just as many simply enjoying a more relaxing, quiet afternoon.
As the waves tended to be a bit smaller than those found 5 minutes away, there were only a couple of surfers in the water. That being said, if you are looking for a less crowded area to learn, this might not be a bad place to go.