Renting a car in Vienna

My preference would be to go by public transport especially in winter. For your itinerary car is not needed. It is a big hassle in big cities. That's the alternative to your idea. Nevertheless here is the answer to your first question: There are many places to rent a car in Vienna. Google them and compare prices. Automatic is more sometimes quite more expensive and not available everywhere. Most rental companies nowadays allow their car to be taken to the Czech Republic and Hungary, but not all. I don't know where you live in the States if you are used to drive on the snowy roads. I would say for experienced driver from the snowy regions it's relatively safe but for someone from Florida, southern California, etc. it's probably not so.

We always rent from Sixt. Good cars, excellent service. That said, I wouldn't rent a car for your trip. Having a car will be a much bigger hassle than getting luggage on and off trains. I promise. I am also a mom with two kids.

From Vienna to Salzburg take the Westbahn train. You buy the tickets on the train from the attendant, kids are 1 euro and there there is free Wifi. The trains are also floor level, so no lifting. 24.90 Euro per adult.

From Salzburg to Prague via CK, I would use the bean shuttle. Let someone else drive and schlepp.

From Prague to Budapest, take the train. Easy. From Budapest to Vienna, take the train. Easy.

Look at the man in seat 61 website for info on which websites to use to buy your Prague-Budapest and Budapest-Vienna tickets.

As long as your kids can carry their own luggage, I see no reason why a rental car would add anything but trouble, headache and excess cost to your proposed itinerary, especially if you've never driven in Europe before. Here's what I know about renting a car in Austria (which I last did in May): The rental agencies charge extra to bring the car into the Czech Republic, Slovakia and Hungary. I'm not sure about the Czech Republic, but the other two require purchase of a vignette, which in the case of Hungary, requires you to register the car electronically. When I rented a car in Austria, the agency would not hand over the keys unless I had an international driver's permit that was explicitly valid in all the countries where I wanted to use it.

To answer your other question, except on some Alpine roads, snow, when it does fall and start to accumulate, is usually plowed very quickly. As long as you don't drive while the snow is actually falling, driving is as safe as any other time. Your proposed itinerary does not involve the Alps, so driving should be fine.

Thank you all for the advice especially to Emily for the link to the transportation.
Now, my plan is to arrive 21, city tour in Vienna 22, 23.

Take the train to Salzburg on the 24th, tour The Sound of Music, Mozart Residence, and Mozart Christmas Eve Concert Dinner.
Question 1: can i reserve the ticket first or just buy at the train station? is Mozart residence near by the sound of music location? Do you think i should book 2 tours (sound of music and Mozart)?

25th, would like to ride a winter sleigh and then continue the journey to Prague.
Question #2: I can't take the bean shuttle to Prague via CK because i have luggages with me and it will be difficult to drag along luggages to do city tour in CK. I contacted Sebastian Tour Transport to drive us from Salzburg to Prague via CK but they are not operating on Christmas day :( any other recommendation on a driver?

26,27 city tour in Prague
Question #3: is the city active or mostly closed?

28 will take the train as you recommended to Budapest.
29,30,31 city tour in Budapest
January 1st back to Vienna

Thank you again.

Question 1: can i reserve the ticket first or just buy at the train station? is Mozart residence near by the sound of music location? Do you think i should book 2 tours (sound of music and Mozart)?

From Vienna to Salzburg you should take the Westbahn train. They do not have a ticket counter at the Westbahnhof as you are supposed to buy the tickets on the train. As an alternative, you can buy the tickets online from their website (same price, though, so no advantage) or from a Tabac shop (these are the shops that sell cigarettes everywhere and there is one in the Westbahnhof). Be sure, though, to get on a Westbahn train, they are blue and green, and not a red OeBB train.

There are a number of shuttle services operating out of Cesky Krumlov that service the entire region--Salzburg to Vienna to Prague. Some will even take you to Budapest. But Christmas is a special time of the year.
www.ckshuttle.cz
www.shuttleceskykrumlov.com
www.czechshuttle.cz
www.shuttle-bus-cesky-krumlov.eu
Have you considered either visiting Budapest or Prague--and spending the extra time in Vienna? It's THE music city of Europe and worthy of a minimum 4 days' visit. During the Christmas season, it's truly a wonderful place.

We visited Budapest-Bratislava-Vienna and Prague last year. We prefer visiting Budapest over Prague.

We did almost this exact same itinerary this summer with the addition of Munich and beginning and ending in Prague. We rented a car as well.
One thing you should think about is the amount of time it will take to drive between cities. When we got the estimates on Rome2Rio as well as Googlemaps, we noted them and thought that the travel times wouldn't be that bad. What we didn't know is that there is a stunning amount of truck traffic on European highways, especially between Prague and the Hungarian border and then again from Budapest to Vienna - it more than doubled our driving time between most of the places on your list. In the winter with the slippery roads I would think it would be even longer.
Parking in all of these cities isn't too difficult; you just really have to plan ahead. Make sure your hotel has parking or at least an agreement with a nearby garage so that you have somewhere to park. Many hotels DO NOT offer this so make that a criteria for where you stay.
Driving in these cities is no picnic either - make sure to rent an excellent GPS along with your car and have your spouse help navigate. If your kids are a distraction while you drive then it could be a bit miserable. If you miss your turnoffs or end up in some warren of one-way streets it can take forever to get back to where you are supposed to be. We had this happen in Budapest and it was not fun.
The only advantage I can see for driving in winter is that you can drop your luggage at the door of the hotel and pick it up there again when you move on. Other than that you are adding a bit of stress to your trip that I think you don't need. The highways between the major cities in this part of Europe are not beautiful or interesting...they really could be anywhere in the western world except for the occasional glimpse of a spire or castle here and there.
Even though it is winter you can pack light and your kids are certainly old enough to drag a carry-on sized piece of luggage with wheels so that you and your spouse aren't having to carry both your own and theirs. The only tricky part will be getting on and off trains but honestly you have plenty of time to make one or two trips up and down the steps of the train to deal with luggage - other than that use taxis to go between your hotel and the train station and it really isn't that big of a deal. I did this by myself when I had a 7 year old. With both you and your husband and two able-bodies kids you should have no problem navigating the trains! I would much rather do that than deal with slippery roads and truck traffic.

December 24 Salzburg closes down in the early afternoon and people go home to dinner -- so keep that in mind in your planning.