Found this interesting - no mention of getting to Williams (WMA) via Amtrak on the Grand Canyon Railway website.
The Grand Canyon is located in northern Arizona. Grand Canyon Railway departs daily from Williams, Arizona, 65 miles south of the world-famous abyss. Coined the "Gateway to the Grand Canyon", Williams is located off Interstate 40, 32 miles west of Flagstaff.
The area is easy to get to via Interstate roadways. However, Grand Canyon Country is a remote part of the United States. The closest major metro area is Phoenix, about 180 miles away or a 2.5 hour drive from Phoenix to Williams. Las Vegas is about a 3.5 hour drive from Williams (233 miles). If you're coming from the Los Angeles area, budget about 6.5 hours to drive to Williams.
If you're traveling from Phoenix, take Interstate 17 north to Flagstaff. At the I-40 interchange go west toward Williams. For added adventure, drive through Sedona on your way north.
Closest Airports
Flagstaff's Pulliam Airport has US Airways (service from PHX) with flights that arrive daily. The next closest airport is Phoenix Sky Harbor, followed by Las Vegas McCarran International Airport (LAS).
If you're traveling by air, planning a trip with Phoenix or Las Vegas is a great way to tour the best the Southwest has to offer. Flying into Phoenix, staying a few nights in the Sonoran desert, and then heading to Grand Canyon Country before heading to Las Vegas for a few more nights is an excellent itinerary that will allow you to experience three completely unique and exhilarating atmospheres.