There is a major transit line that runs right through Hollywood. You can get a train there that will take you Downtown, to the Santa Monica Pier (beach), Long Beach, Pasadena, East LA. USC is 15 minutes on the train. UCLA about 45. Buses run everywhere.
There's a huge transit push in LA and has been for a number of years. It's finally working. No, it's not like Manhattan and it never will be...things are just so spread out, the "last mile" is always a problem. Transfers can take a long time, and the service is less frequent than the NYC subways. So it can be a lot slower, and you definitely can't get EVERYWHERE, at least without a major time investment. But for the first time in decades, it IS possible to live in LA without a car. A lot of people in their 20s and early 30s are choosing not to get cars, and bicycles lanes are exploding.
Downtown used to be a ghost town after 6pm when everybody left work. Now it's bursting with life and entertainment, and is a very walkable place.
You can plan your living situation near your eventual job and your sober living near mass transit.
I'm not saying that LA is the right decision, but being without a car need not be a major factor on moving there.