DH and I are planning our anniversary trip this October to Prague/Vienna/Paris. We plan on flying into Prague and out of Paris (we will be flying from Vienna to Paris also). The only stretch we don't have planned yet is Prague - Vienna!

What would be the best way to travel between these two cities? Plane tickets are pretty high so we were thinking either train or driving.....what would you recommend? (we will be traveling Oct 8th - 18th)

Also does this sound like enough time in each place:
Prague - 4 nights
Vienna - 3 nights
Paris (been there before) - 3 nights

Also how much would you budget to rent a car from Prague to Vienna? I've never driven in Europe (although DH has!)

I'd reccommend taking the train from Prague to Vienna, and then consider either cheap flights or the train to Paris. Check out the cost of train tickets vs. car rental, cost of fuel, travel time, etc. and I think you'd come out ahead with the train. Since you'd be spending so much time travelling, why not consider going to Venice instead of Paris? It may be a lot easier to group cities that are relatively close together to make the most out of your time. As an added bonus, you could spend more time in the cities you listed if you're spending less time travelling to get there. Use a search engine to find car rentals in Europe; the cost will vary according to where you are driving, what kind of car you want, and the enormous drop-off fees in another country.

Definitely take the train. It's almost exactly 4 hours from Nadrazi Holesovice in Prague to Vienna Sudbahnhof on the SC (SuperCity) Train. Sorry, can't remember the price, but it's easier than car rental and dealing with second country drop fees.

From Sudbahnhof Train Station it'a a short walk west (left) on Wiedner Gurtel to the Metro Station at Sudtiroler Platz. Vienna has great public transportation, trams and metro.

I spent more time in Prague, but there was quite a bit to see in Vienna, regret not having more time there. The Hofburg, Schönbrunn Palace and Belvedere Palaces, Karlskirche and St. Stephen's Cathedral, and Secession architecture

Or, if you want to save some money, you can go by bus. It is less than half the cost of the train and takes only about 15 minutes longer. If you consider that it leaves you right in the center of Vienna, it could even be considered faster. We found it comfortable and interesting.