Would you like to take a beautiful drive that will offer you spectacular views and give you a country feeling while still in the middle of the city? Then try driving along Mulholland Drive. Not many cities have a big mountain running through the middle of them, so not many cities have a crest-of-the-ridge drive that has scenic views of valleys to the left and right of the road AT THE SAME TIME! One "valley" is the ocean side of the city, and you can look out over areas such as Beverly Hills, Bel Air, Santa Monica, and Venice. The other valley is the San Fernando Valley--and it's actually an official part of Los Angeles City, too. The San Fernando Valley is home to Encino, Van Nuys, Woodland Hills, Northridge, Chatsworth, and others. (From time to time, these areas try to secede from Los Angeles, but so far the vote hasn't carried that motion forward.) In addition to the wonderful views on either side of you, you'll find yourself in a less-developed part of the city with plenty of greenery and open spaces!
If you stay until nightfall, you'll see thousands of city lights shining in either direction. It's a beautiful sight--and also a sight made famous by The Tonight Show, where you can see a Mulholland view in the opening L.A. photo montage.
My favorite section of Mulholland is from Coldwater Canyon to I-405. To go that way, take Beverly Drive north from Sunset Boulevard--it's easy, because there are signs you can follow. When Beverly Drive splits into two roads, just follow the Coldwater Canyon split up the hill to Mulholland.
Coldwater Canyon is a pretty, tree-lined residential street. Its quiet looks are deceiving, though, because it's actually a major commuter thoroughfare between San Fernando and the "main" portion of the city! I have also accessed Mulholland Drive from Laurel Canyon Boulevard, Benedict Canyon Drive, and Beverly Glen Boulevard, and they're all scenic paths through residential areas that you'd enjoy seeing.
Once you're actually on Mulholland, take care! The locals "drive like maniacs!" The roads are twisty and narrow, but the locals speed along them anyway. (At Disney's California Adventure, there's a ride called "Mulholland Madness," and the term certainly fits!) Luckily, the road offers numerous pullout spots. You can take it easy and make as many stops to enjoy the view as you'd like along the way. I've even spotted deer while in one of these rest areas! I generally leave Mulholland at I-405, but you don't have to. Mulholland goes on for miles and miles. Eventually, you get out into very rural areas of the Malibu hills. Mulholland eventually splits into two roads, Mulholland Drive and Mulholland Highway. If you take the highway split, you can actually keep going until you reach the Pacific Coast Highway!