LA is like any other major city in the US - its fairly safe but you still need to be aware of your surroundings.
There are areas in LA that you probably wont want to venture alone, or in the dark. Ask at your hotel concierge desk of any places to avoid if you plan on exploring. The locals on the ground will have the best knowledge. It also serves to let them know what your plans are so they can keep an eye out for you.
Carry your phone with you, make sure tis charged and have the number of the hotel programmed in, as well as emergency (911 in US).
My saying is "if it doesnt feel safe, it probably isnt". So learn to listen to your instincts. almost 6 years ago
The public transport system is safe, indeed. It's like anywhere else in the world - if you are in a bad neighbourhood, then certainly the public transport system will reflect where you are. But for the daily wanderings of a first time traveller to LA, you shouldn't have any problems. The only problem is, it's not the most comprehensive service in the world - hence why many people get around in cars in LA.
Jesse - Travel Safety Hub almost 6 years ago