If you can afford it La Jolla Shores is also great for families, good safe beach with small current. La Jolla Beach and Tennis Club and The Shores Hotels are both right on the beach, and the Hotel La Jolla is within a 15 minute walk.
Personally, while I love the Mission Bay area, and some of the hotels are truly wonderful, I would not count it as a beach, and the water can be truly disgusting at times to swim in. Just depends on when you hit it.
I also second the Coronado suggestion. Easily the best beach in all of San Diego County (with La Jolla Shores a close second).