What is your budget? That would determine your choices. If your budget is under 1 million $, you likely won't find anything nice, unless it's way way out in the boonies.
Some nice gated communities are Laughlin Park in Los Feliz (most homes are very expensive), La Vina in Altadena, Kinneloa Canyon Estates in Pasadena and Kinneloa Ridge (can't get more private than double gated, you have to go through the gated Estates before you get to the gated Ridge development, and even before the two gates, it's a private street), Malibu Colony, the Oaks in Calabasas (quite a few gated communities out that way, it's out in the boonies), Beverly Park in BH zip code, the Summit, Bel Air Park, Bel Air Crest, Mulholland Estates, Brentwood Circle, and Brentwood Country estates. Most of the homes are significantly over 1 million $.
You speak to a realtor to find a house. Look online at realtor.com, search in the area you'd like to live, look to see the realtors handling that area, their names will be on the listings.
Good luck!