One option is take Metrolink to LA (cheaper than Amtrak) and ride the Coast Starlight to San Luis Obispo. It's a scenic coastal ride for a large part of it, and SLO is a nice small town to visit, with a nice train station.
Going to the Grand Canyon would be a bit of a hassle, since the SW Chief gets into Flagstaff before 5am, then you'd rode a connecting bus and train to the Canyon.
Going to Tucson and a renting a car to Saguaro is an option, or renting a car at Alpine (TX) and going to Big Bend would be fun, too.
You could take the Coast Starlight to the Bay Area and go to San Francisco. Or, go beyond to southern Oregon and tour around there (Mt Shasta, Crater Lake, Lassen, Klamath Lake, the Cascades). A bit further away, Portland and Seattle are great cities to visit as well. I haven't even mentioned Utah or Colorado yet.
Point is, although the Amtrak system isn't super connected everywhere, it can still take you to a lot of neat places, as long as you can figure how to get there.
Edited by ParanoidAndroid, 30 June 2018 - 03:43 AM.
I have ridden Cascades #516 (SEA-STW), Coast Starlight #14 (LAX-SLO), Southwest Chief #4 (LAX-CHI), Cardinal #50 (CHI-NYP), Northeast Regional #85 (NYP-WAS), Capitol Limited #30 (HFY-WAS), Coast Starlight #14 (LAX-PDX), Coast Starlight #11 (SLO-LAX), and many Pacific Surfliners with Amtrak. I have observed, including the previous, California Zephyr #5 at SAC (lucky), what I guess to be Crescent #19 (at WAS) and Silver Meteor #97 (at WAS), Empire Builder #28 at PDX, and Sunset Limited #2/Texas Eagle #422 at LAX. I have also ridden the Hokutosei in Japan, Ueno - Sapporo (now discontinued).