I used to live in Austin but after getting a remote job I moved to LA. I get to live in an amazing, walkable neighborhood and rarely deal with the notorious LA commuting nightmare.
Downtown is great if you want a true urban feel and don't mind the homeless. I found a deal on rent but was looking heavily at Macarther park to Koreatown area.
I've heard parts of Hollywood are good and pretty well connected on transit lines but didn't really explore.
There are many people who live in west hollywood, downtown, santa monica who don't have cars! lyft/uber are also relatively cheap here.