This is just a guess. I think they film in Los Angeles because of cheaper costs since they would have access to the studio sets, and not having to fly stars, guest stars, and crew members back and forth. The producers for all three CSI shows might want to stay close to the filming. But they actually do go out to Miami for a brief time each season for exterior shots. They also have crews go out to film the fly over scenic shots. Miami Vice filmed a lot in Miami. But I guess there are enough California sites that can stand in for CSI episodes in Miami, Las Vegas, and New York.
Yes, i think they go to Miami for all of those shots from the helicopter. When you start the show, or after commercial break, there's always those few moments of film of a birds eye view of Miami's buildings and beaches.
Since the question has been answered correctly, and we have a CSI:Miami Question Thread, I'll go ahead and lock this one. Please don't hesitate to ask any other questions you may have in there. Thanks Dynamo and Hunter.