Many celebrities live and work in L.A. Usually seeing a celebrity is a matter of being in the right place at the right time.
Here are some places where it is possible you might see some celebrities in L.A.
The lobby of the Chateau Marmont Hotel on Sunset. Many celebrities stay at this hotel when in town, some maintain suites there and it's often the place where celebrities give interviews, have business meeting, have photoshoots or just go by for lunch or dinner.
Starbucks in upscale (the Westside) areas of the city.
Urth Cafe
Coffee Bean and Tea Leaf
Ivy Restaurant
Nobu Restaurant (in Malibu)
Beverly Center Mall
Malibu Lumberyard Shopping Center
Malibu Country Mart Shopping Center
International arrivals/departures at LAX
Sports event at the Staples Center
Tapings of TV talk shows
Celebrities are people just like you and me, and they have a right to their privacy. Some will pose for photos with fans, some never do. It depends on the individual and also on how his/her day is going.
Celebrities have good days, busy days, bad days, relaxed days, just like the rest of us. Always observe the rules of common courtesy when meeting a celebrity.