If you poll the locals, they always site Butterfly Beach and Hendry's Beach as the two favorites (which means that they're also popular). Butterfly Beach is in Montecito, directly across the road from The Biltmore: Parking spots are hard-won and there aren't a lot of amenities around, so bring a lunch and anything else you might need for the day. Hendry's on the other hand, is next to The Boathouse, which makes it ideal if you don't like to plan ahead (they have kid-friendly food, plus really solid drinks).
Inspiration Point: Tunnel Rd. & Mission Rd. | Lizard's Mouth: West Camino Ciel Rd.
Inspiration Point is a relatively short hike that doesn't require a huge climb, making it a good option for kids—as its name suggests, there's pay-off for making it to the top, which include great views of the city, the ocean, and The Channel Islands. It's also dog friendly. Meanwhile, Lizard's Mouth is up by Goleta, and is less of a hike and more of a place to go climb around on rocks by the ocean and take in the views (kids love it). Click here for directions—it's not well marked, though as they explain, "If drunk high school kids can find it, so can you." (Image courtesy of Santa Barbara Hikes.)