Train or car or both

If those are the only places on your itinerary I would just take the train. It's less stressful and probably less expensive. A car is useful for areas that are more difficult to use public transportation. Think Tuscany, Provence, etc. Your itinerary doesn't include anything like that.

A train trip from Geneva to Vienna will take approx 11 hours (8:30 to Salzburg). I'd look for a budget flight (sykscanner, kayak etc.; for an initial overview go to rome2rio). Vienna to Prague is easily doable by train in 4 hours; flying won't save much time.

1) A car is useless in Geneva, Vienna, Prague or most other big cities.
2) Hiring a car in one country and returning it in another usually incurs a large surcharge. Or were you planning to drive back from Prague to Geneva?

Geneva to Vienna is too long for a train, lots of flights though (Austrian Airlines and Easyjet). Vienna to Prague is good by train (4 hours, see here: https://www.seat61.com/trains-and-routes/prague-vienna-railjet-train.htm )

But, you say "Geneva to Austria, Vienna and Prague", do you have somewhere else in Austria planned?

Where are you flying out of? Flying "open jaw" out of Prague would be obvious. Did you actually want to go to Geneva? It is not the obvious choice in Switzerland. Or did you just book the flight thinking Geneva to Vienna was a short distance?

there is another thread where poole_ta is going Geneva>Luzern>Bern>Füssen>Salzburg>Vienna>Prague>Geneza all in 2 weeks.

Like what Chris said. If all you're planning is to visit the cities, don't get a car. You only need a car if you plan a lot of stops in between the cities and your itinerary would be difficult (or impossible) to do without a car.

I rent a car virtually every trip now but that's because, over time, my itineraries have become more compact and include multiple stops in a day as well as a lot more stops that are out of the way without a car.

SO many of you say take the train.
Here is the trip. Flying into Geneva-staying 2 days-would like to see Lucerne and spend the night. Then going to Neuschawnstein for a night and seeing the castle. On to Salzburg for 3 days. On to Vienna 3 days On to Prague 3 days, and then a stop in some German city on the way back to Geneva. I have 1 more day to put towards one of the cities. As for trains, how do I even know how to start with that. If we got a car the plan was to return to Geneva. If you think trains are doable, could you please tell me how to start with booking them. There are 4 of us. And to trains go out to Neuschwannstein. THank you

I would say that your itinerary needs some work. You have nice places but they involve some quite BIG places and you have a lot of BIG distances to cover. In 2 weeks? Doing this by car isn't absurd, but almost.

I would start by arranging a flight from Geneva to Vienna with EasyJet, or perhaps to Prague. Then you can work your way back by train. There are flights from Geneva to Vienna on some dates for less than $50. I see some flights to Prague on Swiss for about the same price (check Google flights.) You have provided no travel DATES or passenger info (ages) so we can't make specific flight or train journey suggestions yet. You can get an idea of train travel times using the DB itinerary search page (which has connections for all of Europe.)

Switzerland, Austria, Germany and Prague are all marvelous, but you probably have too many locations in mind. I would seriously advise dropping Neuschwanstein (I know you have tickets... but it's way too much trouble to get there for a 30-minute tour of a late 19th-century palace, not a castle at all. Do a day trip there from Munich if you cannot talk yourself out of it. Train to Füssen + bus connection to castle stop + 1 hr. round trip walk - that's about 6 hours of "going time" round trip though.) And drop Vienna too (meaning that after Geneva, you would fly to Prague.) Then you'd have this much more doable itinerary, about right for 2 weeks...

Geneva...
Prague...
Germany (Nuremberg, Munich and/or Regensburg would be logical)...
Salzburg and surroundings (Several good and REAL castles thereabouts!)...
Lucerne...
(and back to Geneva)

And if you can squeeze out a night or two in the Bernese Oberland (Interlaken, Lauterbrunnen area) on the way to Geneva, you'll be stunned by the great scenery there.

For city center to city center a train (or plane for long legs) is your best bet. A car is handy when you make lots of intermediate stops, especially if they aren't well served by public transportation. It sounds like you are going city to city so compare trains to planes (and possibly buses) and decide what works best for you.