Los Angeles can be confusing to newcomers in that Downtown isn't the center point of the city. Rather, the city is more a juxtaposition of disparate communities that loosely form a metropolis (67 suburbs searching for a city, so they say). The best way to grasp the geography of L.A. is to break it into six regions (it's time to tear out that map tucked inside the back cover): Santa Monica and the beach communities, L.A.'s Westside and Beverly Hills, Hollywood and West Hollywood, Downtown, Pasadena, and -- on the other side of the Hollywood Hills -- the San Fernando Valley (just "The Valley" to locals).
Each region encompasses a more or less distinctive patchwork of city neighborhoods and independently incorporated communities. West Hollywood, for example, is its own incorporated city, whereas Hollywood -- literally across the street -- is part of the city of Los Angeles. But don't knock yourself out trying to remember all of this: To visitors it's all the same.
Most visitors arrive at Los Angeles International Airport (LAX), located on the coast just south of L.A.'s primary beach communities. Unless you're coming to L.A. on business, you're likely to concentrate your visit in the city's western districts, since that's where the majority of tourist attractions, restaurants, and shops are located. In fact, most visitors never make it as far east as Downtown, although it would be a big mistake to miss seeing the new Walt Disney Concert Hall, one of the most impressive modern architectural achievements in the world (really).