The first question to ask – what do you want to see or do while in Los Angeles? Will you be traveling with children? Do you like great restaurants? Are you a clubber? Most important: will you have a car while in L.A?
Hollywood is a good base for those who want to be near the Walk of Fame and Universal Studios – it’s also convenient for those who don’t want to rent a car and are relying on public transportation. It’s also great for those who like the club scene (see L.A. FAQs Nightlife). Much of Hollywood is safe, but use care at night if on foot. It is, however, very safe for families.
West Hollywood is central to both Hollywood and Beverly Hills, and hotels there tend to be within the residential areas. West Hollywood prides itself as being it’s own city, and has a large gay community.
Beverly Hills (and Century City) is also a great central base and is closest to the beach while also close to Hollywood. You would be advised to get a rental car, but it’s okay to rely on public transportation – just expect longer travel times. It’s a great place for families, but it’s expensive.
Santa Monica is one area that can be explored on foot. There are lots of shops, restaurants and bars within walking distance, and tends to be a very safe place. Venice has some sketchy areas, use care at night. While there are tours that commence in Santa Monica, you are about 45 minutes away from Hollywood tourist sights. Also great for families, but hotel rates are higher at the beach.
Downtown tends to be the most reasonably priced area, but you will be doing a lot of traveling to see sights. You are furthest from the beach, but with a renaissance in Downtown LA, there’s a great nightlife and some of the city’s best restaurants.