A storm washed out the train tracks in San Clemente, and Amtrak has been running a bus bridge between Oceanside and Irvine with a reduced schedule. I think they're currently expecting tracks to be fixed by February, but that's already been delayed twice, so I wouldn't count on that. As long as the tracks are out, luggage handling is limited, so if you can't carry all your own stuff, the train might not be a good option.
Usually the cheapest way to get from here to L.A. when there's more than one traveler is to do a one-way car rental and just drop the car off there. That's what we do for flights and cruises. It's not at all hard to drive to downtown L.A, and you really don't have to worry about getting lost if you do it in the daytime. Also, if you pick a hotel that has a car rental on site or nearby, you can just drive there, drop off the car, then get an uber or taxi when you want to go back to the station.
I personally like staying at the Omni Hotel downtown. It's about a 10 minute car ride from Union Station, and it's in walking distance to Angels Flight, Grand Central Market, the Disney Concert Hall, the Bradbury Building, the library, the Last Bookstore, etc. You could easily fill a couple of days there if you have that much time.
If you want something really iconic, it's only about 3 blocks further to the Westin Bonaventure. Or if you want to be closer to Union Station, there's a Doubletree in the Little Tokyo area just south of the station.
