The beaches in Carlsbad tend to not be white sandy beaches. They are often covered in sea weed and have little sand.
Oceanside (next town north of Carlsbad) has a nice beach next to the Oceanside harbor. There is a large sandy beach with palm trees. There are shops and places to get food behind the beach in the harbor. If you want a family meal at the end of the day, you can walk to the end of the Oceanside pier and eat at the restaurant there.
If you want to head further north, go to Crystal Cove State Beach in Laguna Beach. It is very spread out. Make sure you park in the parking lot next to the historic district. From that lot, you can walk down to the beach or take the shuttle. There are 2 places to eat at the beach there and there are beach equipment rentals on the beach. You'll have beach as well as tide pools.
Not too far south of Carlsbad is Cardiff by the sea. They have a long stretch of beach with paid parking lots at each end. There can be a lot of piles of sea weed there, though.