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Hi Patricia. First of all, it’s great that you’ll be making the beautiful Glacier Express trip!
As for hotels: this topic on hotels in Zermatt may help you out, to start with. Personally I can add the Alpenstern hotel, which is very close to the main railway station. It’s quite simple, but just fine for an overnight stay. Further hotels can be found in our hotel list.
This goes for St. Moritz as well. I don’t have any personal experience with hotels there, but I do know that most hotels in the town centre and close to the main railway station are rather expensive. Instead, you may want to opt for an overnight stay in a nearby town. Towns as Celerina, Samedan and Bever can easily be reached by train within only a few minutes from St. Moritz, and they offer more affordable hotel options. Please take a look at the cheap accommodation page as well.
I hope this gets you started. Good luck on your further preparations!