My husband and I will be leaving Budapest January 7, 2020 and our flight back to US is January 12th at noon. We want to experience as much of Switzerland as possible by train and include a ride on the Glacier Express. Should we take the train from Budapest to Chur/St. Moritz and take the Glacier Express from there to Zermatt? Then work our way to Zurich? This would enable us to see some of Austria. Or save the time and fly to Zurich and start our Switzerland tour from there? What are the must see things along either route?
What airport are you using to return to the US? You have a lot more sights than really four full days will allow. Definitely fly from Budapest to Zurich. Next day be ready to take the train from Zurich to Zermatt, that will 4+ hours of travel time by train. You will want to spend at least one full day in Zermatt. Next day take the Glacier Express from to Zermatt to Chur or on to St. Mortiz. Last day take the train back to Zurich. Not a lot of time to stop and look around, going to be more of a drive by tour.