The public transportation in LA is alright. Hopefully, you'll be close to the Metro. You should look into buying a couple of weekly passes - the MTA will sell you a card for about $15 a week that gives you unlimited access to the light rail/subway and buses. Which reminds me, you should take it to Downtown LA. There's lots to see and photograph there. A real favorite is the Bradbury Building. Nondescript outside, but inside is one of the most beautiful buildings anywhere. You'll recognize the open cage elevators from Blade Runner and many TV shows, commercials and movies. Same with the Second Street tunnel. In the US, at least, every car commercial seems to be partially shot in there. Ride the Angel's Flight funicular, visit Grand Central Market, the Central Library, and give yourself several hours to wander. Casey's is my favorite bar down there and the Yorkshire Grill is my favorite place to eat - they will have vegetarian meals, too. Another great restaurant is Engine Company No. 28, and be sure to drop in at the Biltmore and Bonaventure Hotels.
You can also take the Metro to Long Beach. Pine Street has wonderful boutiques and restaurants. For real local color, visit Roscoe's Chicken & Waffles - at least have a waffle there. From Long Beach, you can catch a boat over to Catalina Island. It's slightly touristy, but stunningly beautiful. A tour of the art deco Casino is a must and you might want to take a trip to the inside of the island to see the buffalo colony. Though not as easy to get to, you can arrange a trip to the Channel Islands. They're uninhabited nature preserves and just stunning.
If you want to venture a little further, a night out in Death Valley would be fun. There's a ton of interesting stuff out there, from the salt flats, the Rhyolite ghost town, Pupfish (very unique), Scotty's Castle, and much else. Other day or overnight trips that are worthwhile are visiting Santa Barbara or San Diego, each roughly two hours out.
The rough parts of town are generally inland from the coast. Most are OK during daylight hours and most people aren't aggressive. A friendly, "hi, how are you?" with a smile will get you by. You'll also find a lot of sheriffs on the Metro, too. Don't be afraid to wander into the Jewelry District downtown. It's not as gentrified as other parts, but there's usually a ton of people on the streets and I've spent many a lunch hour wandering there. Oh, and if you go a bit east of there, there's an artist district and a few galleries in the old warehouses. A cousin lives down there and I occasionally hit the shows. I would not walk there at night, but a cab can get you to and from downtown for a few dollars. It's worth seeing.
