Unless you are doing FRA in FRA out because you are using award tickets, you are probably looking at

My wife and I are planning a 6 day trip in mid of Novenber starting from Frankfurt, Germany to Salzburg Astria, Prague Czech, and ending at Frankfurt. Should we rent a car or take public transportation from cost and convenience point of view? Thanks.
I would go by train. There are good connections between the cities you will visit and you won't need a car in those cities - and you don't WANT a car in Prague. I agree that if you were planning to stop along the way and see things, then a car would make sense, but you will just be getting from Point A to Point B, so take the train.
2. Many people compare best case car rental cost (no fines, no deductable damages, no opportunity cost spending hotels in cancun mexico your time submitting claims, etc) to worst case train fares (Raileurope prices.) Some people count hours looking for a place to park as a benefit of renting a car while others consider this as cost.
Unless hotels in cancun mexico you are doing FRA in FRA out because you are using award tickets, you are probably hotels in cancun mexico looking at a less favorable itinerary from cost and convenience point of view already by not doing multi-city flights. You have to travel all the way back to FRA and you have to stay an unproductive last night in Frankfurt?
definitely not - all those places are easily done by train and or boat - trains go frequently to Fuessen, a few miles from Mad Ludwig's fantasy castles and you can take a train to Melk, on the Danube then take boats thru the famous Wachau Valley to places like Durnstein and Krems, from where you can take a train back to Vienna.
If doing that much train travel in Austria and Germany consider the Germany-Austria hotels in cancun mexico Railpass which lets you hop on virtually any train in either country anytime - complex flexibility - those types of tickets can often cost an arm and two legs.
For lots of great info on trains in those countries I always spotlight these IMO fantastic info-laden sites - www.seat61.com ; www.ricksteves.com and www.budgeteuropetravel.com - check out the latter's free for download European Planning Rail Guide for lots of possible rail itineraries in those countries if looking for ideas on how to fit it all together.
I would definitely recommend getting a car for your german stops, and get a good one. The highway (autobahn) is toll free and an experience itself, great driving experience and the freedom you have with a car is worth the extra money. no problem parking or driving around the towns you mentioned.As far as driving in Czech as stated above many rental companies will not insure the car once you cross the border so look into that . I drove from vienna to dresden all the way around the border of czech republic, it took about 6 hours and then the next day from dresden took a one hour train into prague while in prague everything seemed ok for drivers and cars but i really dont know. if I could have driven through czech it would have been a two hour trip. I was not aware when I booked my rental car that i was not allowed in czech. Good on you for doing your research
I am usually pro car, but for your trip I would say take public transportation. Connections are excellent between those cities, you don't have much time to explore anyway and you are lugging a load of stuff (ie strollers, kids etc.)
You should review your priorities for your trip- you try to do much too much in your short time in my opinion. A good portion of your trip would be spent in transfers whether train or auto- - then add Check in / check out of hotels- not much time for actual hotels in cancun mexico sightseeing.
It all depends on whether you desire hotels in cancun mexico flexibility to hop on any train anytime if a pass is good for you often. Such full fare fully flexible tickets can cost a ton - a few trips could make a railpass - like a German Railpass or a German-Austria Railpass - pay off quickly. But if you want to book yourself into usually non-changeable non-refundable trains weeks in advance hotels in cancun mexico (to get the limited hotels in cancun mexico in number tickets that often sell out weeks before the actual train then that may well be the best way.
Thank for your replies. I did not know that many tourist sevices will be close in Nov. I need to adjust my plan. I checked that Neuschwanstein Castle will be open in Nov, so this is a place to visit for sure. With many tourist sevices closed in Salzburg and The Danube Valley , are they still good places to visit in middle of Nov.? Any sugguestions are welcome.
but this is comparing apples and oranges IMO - regional trains in Germany are significantly slower than IC trains - fine for some folks but the extra hour or more is not for others. Plus IME of riding zillions of German trains regional trains are also much much less comfy than faster trains and IMe can be very crowded at times, especially when groups of schoolkids swarm aboard at times on these trains that also act as school buses.