Having been to LA a few times, I can tell you that Venice Beach is not a child-friendly place at all! Luckily, Santa Monica is and it was fantastic spending time there. Other family friendly things to do in LA I would suggest are the Griffith Observatory, the Hollywood Walk of Fame, the Natural History Museum and California Science Center.
There are many places to explore with family: Disneyland Hollywood Olvera Street/Union Station Santa Monica Beach and Pier Griffith Park Los Angeles Science Center Discovery Science Center, Santa Ana Los Angeles Children’s Museum Legoland, Carlsbad Places to eat: In-N-Out Burger: Multiple locations, best burger in LA, ask anyone. Pink’s Hot Dogs: 709 N. La Brea, just north of Melrose. You might even see a celebrity. Maybe. Tommy’s Chili Burgers: Look for the shack, an LA tradition. The original location is at Beverly & Rampart, a couple miles west of downtown. Canter’s Deli: 419 N. Fairfax, between Beverly & Melrose. Near CBS, you might spot a celebrity. Phillippe’s: 1001 N. Alameda. Great roast beef sandwiches. Near Union Station and Olvera Street. Watch the mustard, it’s hot. Tito’s Taco’s: Voted best tacos in LA, even though it’s in Culver City. King Taco is a good alternate if you can deal with East LA. The Pantry: Corner of Figueroa and 9th, downtown. Huge portions, they never close, GREAT steak and eggs. Medieval Times and/or Pirate’s Dinner Adventure: Dinner and an adventure show, both are on Beach Blvd in Buena Park, you get to eat with your hands. Places to Shop: Third Street Promenade, Santa Monica The Grove, Los Angeles Americana @ Brand, Glendale Beverly Center, Los Angeles Citadel Outlets, Commerce Brea Mall, Brea The Block at Orange, Orange South Coast Plaza, Costa Mesa Fashion Island, Newport Beach