Hi- I have a daughter studying abroad this summer in Prague and would love to visit as well as tie in a trip to the Alps with my son. Do you think our best option is to take the 7 hour train to Innsbruck, Austria? And if so, what other towns do you recommend when in the area? (We will also hit Salzburg, for sure). Would it be best to fly to Switzerland or France rather than train to Austria? And we only have about 9 days to do it! (I know, eek...we will barely scratch the surface). Thanks for your insight!
If you have the option, it is easiest to explore the Austrian Alps with a rental car. It allows greater flexibility and time savings in getting to trailheads and small villages. Ehrwald and Zell am See are beautiful. The drive by the Grossglockner through Heiligenblut is supposed to be spectacular. If you don't want to hike, there are often trams and ski lifts that will take you high on the mountain. The food at the mountain "huts" is often some of the best in Austria. Austria is typically less expensive than Switzerland. If the Austria Alps is your destination, I suspect that a rental car from Prague is the quickest way to get there followed by train but I haven't looked into flying from Prague.
The following websites (among others) provide information on sightseeing, hiking and other activities in the Austria.
https://www.tyrol.com/
https://www.moonhoneytravel.com/
https://www.austria.info/en-us/
Do the 9 days include traveling from/to US, and visiting Prague and Salzburg? If yes, there is not much time left for the alps, i.e. I would go to an area easily reachable from Salzburg.
The Alps are just 1 hour south of Salzburg on the S-Bahn.