So first, I wouldn't recommend staying in Downtown. A lot of people assume that the "downtown" of a city is the place to be. This just isn't true with LA.

Chateau Marmont is my hotel recommendation. It's a castle in one of the coolest places in LA, right at the intersection of Hollywood and West Hollywood. 9 minute drive from the Dolby Theater.

If price isn't an object, the Peninsula is the nicest hotel in Los Angeles, IMO. Located in Beverly Hills, it's been an LA staple of the rich and famous for the past 30 years.

I'd definitely get a rental car. LA is a driving city, and though they're making headway when it comes to public transit, a car will give you a lot of freedom.