Hi James& Bette. Unfortunately, there is no Amtrak service in Phoenix. Here you can find all Amtrak stations in Arizona and select which is closest to you https://amtrakguide.com/stations/amtrak-stations-in-arizona.

Here you can find all Amtrak train routes, so maybe you can consider other cities. https://www.amtrak.com/train-routes

To get the best price, you will need to buy tickets in advance and also you should be able to get a 10% seniors discount.