We will be flying into Frankfurt and indend to visit Vienna, Prague and Budapest. We expect to travel by train but could be convinced otherwise. Based on the train schedule I've looked at, Vienna looks like the easiest first stop but it seems we'd eventually be backtracking. Any recommendations about the sequence and mode of travel?
Unless you intended to spend time in Frankfurt I would suggest you fly on to Prague. Should be plenty of connections. Then I suggest you do Budapest last because its the most laid back of the three; while Prague is the most crowded and an be somewhat intense. If you want to go by train I would still suggest you just bite the bullet and take the long train haul from Frankfurt to Prague; but you will be trading an hour flight for 6 to 8 hours and a couple of transfers on a train.
On such a trip, flying open jaw is the only way to go--in time and money.
We're getting ready to fly into Budapest on the way to Bratislava, Vienna and Prague by train.
I just hope you've not yet made your flight arrangements.
Otherwise, James is right about what to do. Check Czech Airlines airfares between Frankfurt and Prague.
I see a number of problems with your plan.
First, a train from FRA to Prague, full fare, will be quite expensive. You could save a lot with an advance purchase Savings Fare, but that is pretty risky right after a trans-Atlantic flight due to the chances of a late arrival, because those fares are for a specific train and non-exchangeable, non-refundable.
Likewise, if you fly to Prague, you'd better book a continuing flight from Frankfurt to Prague because a second airline might not honor your ticket if the arriving flight is late. If you come in on Lufthansa and go on to Lufthansa, the next flight to Prague, after the one you are booked to take, could be as much a three hours later.
If instead you fly into Munich (MUC) there are some other options. You could fly on to Prague with a continuing ticket.
There are four Bahn IC buses from Munich to Prague. One even stops at the airport, but it is in the afternoon. The lowest fares are only valid for the bus you book, so, again, risky with the probability of a late arrival. A full fare ticket costs 72,20€ including the S-Bahn from the airport to the bus station at Hackerbrücke.
There are number of regional train connections per day from Freising Bahnhof (a 20 min bus ride from the airport) to Prague. Two of them, at 9:09 and 13:09 take 5½ hr. With a Bayern-Böhmen-Ticket to Pilsen and a Czech Rail ticket from Pilsen to Prague, the fare is about 30€ for one person, 40€ for two. Bayern-Böhmen-Tickets (26,00€ Single, 30,50 for two) are always available and can be purchased at an automat in the Munich airport or at the counter for 2€ more, and would include the bus to Freising. Buy the Czech ticket from the conductor in the Czech Republic. The Bahn charges two to three times as much.
Yes, going from Frankfurt to Vienna as the first stop among the three cities is the easiest since it's direct and on the ICE train.
I've done this route day and night, the ICE day train is preferable. I would see Budapest as the last place since getting back to Frankfurt from Budapest you can do with just one transfer, ie at Vienna (Wien Westbahnhof). Both legs are on fast trains, the RJ for Budapest-Vienna, the ICE Vienna-Frankfurt..
Another possibility, if sleeping on a train is not a problem for you (it isn't for me), is to spend the day in Frankfurt and then take the night train (CNL 459) from Frankfurt Süd (south) Bahnhof (just before 1 AM) to Prague (10:31). Or, you could spend the day in Heidelberg, then take the same night train from there at 11:33 PM.
To avoid backtracking fly from Frankfurt to Prague, then train to Vienna then Budapest. Fly back from Budapest, so called open jaw.
llja; I am with you on that one.