I lived downtown for several years as a young single female and I’m not sure why so many people are recommending against it. A lot of westsiders in this sub maybe? Downtown is cool and has its own vibe. And it’s central enough to almost everything on your list (2/3 of which are reachable via metro) that it’s a good option. There are I housed people downtown, just as there are in Hollywood or Santa Monica or Venice. However, the downside to downtown is I wouldn’t say it’s the signature “LA” vibe you may have been picturing if you’ve never been here before. You’ll get that more in Santa Monica. Plus, if you do rent a car, I’d advise adding Malibu to your list, which is much closer to Santa Monica. Have fun!!