Go to the top level of the Hollywood and Highland Center, which sits on the northwest corner of Hollywood Boulevard and North Highland Avenue. The center, which is the same neighborhood as the Grauman's Chinese Theater and its Walk of Fame, was designed to give visitors several good angles of the sign.
The intersection of Franklin Avenue and Gower Street has a decent view of the sign, as does Lake Hollywood Boulevard.
Visit the Griffith Park Observatory, which overlooks the entire Los Angeles metro area. The park, which includes the Los Angeles Zoo. There is no cost to tour the observatory, and many a photo is taken from there. The best angles are on the west side of the observatory.
Try Beachwood Drive at your own risk. It has several good views of the sign while the car is in motion, but there are no good places to park and take a photo. The best look at the sign is at the intersection of Beachwood and Scenic Avenue. The next best bet is to go all the way past Glen Oak Street, try to park, and climb a small hill for a clear shot of the sign.