Another option is to get off at the Burbank Airport station. There's a Marriott right at the airport and a Courtyard not too far away. I know the Marriott has a shuttle (although it's not much of a walk), and I think the Courtyard does too. You can sometimes get very good rates. If you're coming in on the Coast Starlight or a Surfliner from the north, it's the last stop before LA Union Station. Metrolink trains or the Surfliner can get you to Union Station in the morning -- it's a quick hop. If you're coming into LA from the east or south, you'd have to make a connection at LAUS going the other way, but you could pick up the Starlight at Burbank the next morning.
One potential problem: Burbank doesn't have baggage service. There are hacks for that, I think, like buying a ticket and checking baggage through to LAUS, but getting off at Burbank and picking it up the next day. I've never done it -- there are people on this board who know a lot more about that, though.