Others have answered the question you actually asked, but I'll throw in a different option. You can get off the Chief at Albuquerque and hop right on the Rail Runner at the Amtrak station, the Alvarado Transportation Center (see
Downtown Albuquerque | Rio Metro Regional Transit, NM). Frequent and fast service to Santa Fe. Pro: You get to ride another train, always a treat for us railfans. Con: You'll miss the lovely little station at Lamy (and the shuttle). Your choice. The Rail Runner's Santa Fe Depot is about a half-mile from the Plaza, the center of historic Santa Fe and the famous St. Francis and LaFonda hotels. Not too far to walk, but if the weather's dicey (possible though unlikely; my experience is that even if the thermometer reads chilly, the brilliant desert sun makes it feel otherwise) or you're burdened with luggage, you could take a taxi or Uber or your hotel would pick you up.
And no car rental! You'll need one if you want to explore northern New Mexico, which has some of the most stunning and varied topography anywhere. But Santa Fe is very walkable and interesting.
Eat at Pasqual's,
https://pasquals.com/, and walk off the calories.