You might want to visit the Walk of fame, Universal Studios Hollywood, Cabana Club, Element Club, Mood Club, Hollywood Movie palace, Los Angeles Farmer's Market, Sunset Strip, Kodak Theatre, Hollywood Blvd.
The Ivy is a very popular place for celebrities to eat lunch. Rodeo Drive in Beverly Hills for shopping, also try Wolfgang Puck's restaurant, and night club, The Viper Room.
There are lots of places near Beverly Hills where you can see your favorite stars and not only that, you can also see where they live because most of Hollywood celebs have a crib in that place. Sometimes, you can just drive past them and greet them with your biggest smile.