Here's a crime mapping tool from the LAPD that shows the location of criminal incidents.
CrimeMapping.com - Helping You Build a Safer Community
Crime Mapping and COMPSTAT - LAPD Online
I was a little reluctant at first to share this, because it makes LA look like it's the East End of London during the Jack the Ripper era, but things aren't really that bad. The default is to plot crimes over the last week, and it looks like the place is really dangerous. But you can also specify plots for individual days, and all of a sudden, the reported crime virtually disappears. You also can select out the crimes which might be of most interest to someone staying in the area the night before boarding the train -- stuff like assault, robbery, and homicide, and those crimes are even more rare. (And assault is a very tricky one to interpret, as the legal definition of assault can consist of touching someone's arm during a heated conversation.)
Unfortunately, word of mouth and media reporting of safety issues in big cities tends to overestimate the risk from violent crime. First of all, no one compares crime rates with the rates of injuries and damages from traffic incidents. Secondly, reporting in the media is quick to emphasize when one of these incidents occurs in the city, complete with live video. I mean, our local news reports in Baltimore always seems to lead with news of some shooting (usually not fatal, but often is so), and one might get the idea that if they stepped one foot in Baltimore City, they're going to get shot and beaten up, but I've lived in Baltimore City for over 40 years and the worst I've had is my car broken into (they didn't even bother to steal it.) I spent years walking from the light rail at Mt. Royal to Penn Station at 5:30 AM and never had any trouble. I imagine the part of Los Angeles around the train station is a similar area. And one would certainly be pretty safe within a reputable hotel in the area. I've only been in the area around the LAX station once, and it didn't seem like it was a particularly rough neighborhood.