Hi! New to La :) Any pointers?

Hello Everyone! I am excited to be in LA and not in the snowy cold east coast as I usually am. I love the area, but it is so overwhelming choosing an area! I see That West La is pretty popular along with Beverly Hills, west Hollywood, and Hollywood. What exactly is West La? Lol I have stayed in the Brentwood area right ofF the 405, but doesn't seem to be that great of a location. If any of you have hotels you have felt safe in and are upscale in any of the areas especially west Hollywood/Beverly hills that would be a GREAT HELP to me. I am determined to get this right I don't want to be in the cold  east coast! lol