Looking for best strategy for visiting Vienna, Salzburg, Prague and Venice

If your daughter and SIL only have 10 days total, then you would only have 8 days in Europe to sightsee. In the best of situations that would only give you 1 1/2 days in each place. Not much time, and a lot of sitting in trains, especially a full day getting from Austria to Venice. Prague would be the outlier, you might consider dropping Prague if you can't start there. You don't need to fly from Venice to Rome. There are high speed trains between the 2 cities. But why would you go there just to fly home?

There are many trains per day from Venice to Rome. Some take only 4 hours. I'd definitely prefer that to flying.

Here are the times for the other potential travel legs:

Vienna-Venice: 7:40 (leaving around noon, direct) or significantly longer (and with multiple changes)

Salzburg-Venice: about 6:00 (leaving at 8:12 AM, direct) or longer (often with multiple changes)

Vienna-Salzburg or vice versa: about 3:00 direct

Vienna-Prague or vice versa: 4:00 to 5:00 (direct or one change)

Salzburg-Prague or vice versa: 5:00 to 7:00 (at least one change, best via Linz)

Prague to Venice would take 12:00 or longer with at least two changes, not necessarily via Salzburg or Vienna

I used TheTrainline for this research for convenience, since three countries are involved. I'm hoping it presented all the good alternatives.

Your plan to start in Vienna, in conjunction with the desire to travel from Austria to Italy by train, is going to cause a great deal of wasted time on this trip. Prague is well north of Vienna; Venice is south. You are looking at over 20 hours on trains to travel Vienna-Salzburg-Prague-Venice. That's just too much time for transportation when you have only ten days for this part of the trip. You really need to either fly into Prague to begin the trip or fly from Prague to Venice. That latter is the change that would make the most difference.

I appreciate your suggestions so far!

We spent 4 days in Rome two years ago, so the extra days without our daughter and son-in-law would be a bonus for my history-loving husband (and me!).

We traveled by train in Italy and found them to be excellent. We also took an early morning flight from Florence to Paris, so inter-city flights are something we'd consider. The train from Austria to Venice would be for the WOW factor of seeing the Alps by daytime (a first for all of us) as we descend into Venice.

As for Prague, I can see the problems with the distance, so was thinking that flying there from either Vienna or Salzburg would be a more economical use of our time. I am under the impression that flights directly into Prague from the US are considerably more expensive than into Vienna.

We aim to spend two days in each of the four cities.

most time-efficient order of visiting these 4 cities?

Vienna to Prague by air or train. Even with security, etc. air will probable be a little (an hour?) faster. One hour plane, four hour train.
Prague to Salzburg by air. An hour our two faster connecting through Frankfurt. Otherwise you connect through Vienna for the faster trains. Four hour plane with connection. Seven hours train with connection.
Finally, Salzburg to Venice per your desires, by train.

Agree that you are traveling more than I like over 10 days. However, this isn't my trip.

Thank you for another helpful observation!

I am under the impression that flights directly into Prague from the
US are considerably more expensive than into Vienna.

Impression or you checked and confirmed?

I think logic for efficiency is Prague to Vienna by train, then Salzburg and Venice by train. None of the train rides are partucullarly memorable as for the sights out the window. Bring a book. OR, Vienna, to Salzburg to Venice by train and a flight to Prague.

You might look for at least one more stop. Some place interesting and memorable.

Check train schedules carefully. There's a 5:28 EuroCity/RailJet routing from Prague-Salzburg with a change in Linz.

Thank you for the suggestions and advice.

It's difficult to compare airfares because we can't book flights for a year from now, so any research done now is going to be guesswork. (I was shocked to find flights with 8+-hour stopovers!)

I'm guessing that train schedules are probably more stable over time.

Our daughter planned a ten-day trip for us two years ago, flying out of Toronto to Rome, and home departing Paris, returning to Toronto.

We live in Cleveland. We can fly out of Cleveland, Columbus, Detroit, Pittsburgh, or Toronto.

I appreciate the train info and the time comparisons (train vs local air travel) you provided and will pass that along to our daughter. Again, thank you!

I think you will find it easier to travel Prague, to Vienna, to Salzburg, to Venice. That's fairly easy by train. Just my personal experience.

I'd leave off Venice, because you're going to run out of time unless you have more than 2 weeks. But you might consider flying out of Munich, which is an easy train ride from Salzburg; the fares may be better.

Okay, then let’s say you and your husband have 9 full days in Europe since you can be gone a bit longer.

Day 1, arrival day in Venice
Day 2 Vencie
Day 3 mostly traveling to Salzburg
Day 4 in Salzburg
Day 5 mostly traveling to Vienna
Day 6 in Vienna
Day 7 mostly traveling to Prague
Day 8 in Prague
Day 9 depart

If that is too rushed for you, you will have to drop a city or find a few locations that are closer to each other. Salzburg, maybe Hallstatt, Vienna and Budapest. Half the travel time of your list. But its all about what you enjoy so there is no wrong. But thats a tad rushed for my taste.