Subject: travel from Amsterdam to Vienna

We are not real experienced European travelers. We have made two short trips so I am looking for your expertise and advice.

We are visiting our daughter living in Vienna in October and our son happens to be in Rome for a semester of study, so we hope to combine a visit to both. We have been to Rome before, so we won't spend as much time there this time. We have airfare to Amsterdam and would like to know about the best and most economical ways to travel to both places. I have heard the train from Italy to Vienna is great.

Thanks so much, Lynne Gig Harbor, Wa