Driving trip--Hungary-Czech Rep.-Poland

I can create over thousand itineraries for you so can other posters. Give us some thread, look at the map what's on your way, google it and have at least some idea about your route. Which country to start? It really does not matter. I would adjust it based on convenience of flights and price. Car will be significantly more expensive. If you go by train and you want to stop in smaller towns on your way then Budapest, Bratislava, Brno, Prague, Olomouc, Krakow. Bratislava, Brno, Olomouc are not exactly small towns but smaller than your three cities.

I had seen an answer someone who suggested their route change because they were backtracking too much, which is why I asked about where to start and end as well as length of stay in each city. I also am curious if people have driven the route between these cities/countries and if they recommend doing that over train travel.
I should also have mentioned I am interested in textiles and beads, and I want to search out towns rich in the arts.
Perhaps I need to wait until I have done more research and planning before asking questions.

Patt, have you reviewed the RS Guidebooks for Poland, Hungry and the Czech Repbulic? We've used Rick's Guide books extensively in designing our driving itineraries (~ 20 trips with car rentals for precisely the reasons you've stated); once I've the rough framework in place I might look for additional suggestions for destination experts on the RS Travel Forum or other similar sites. Once I started to plan Prague to Budapest (via Vienna), Rick had identified many so wonder small towns we finally decided to expand our itinerary into two separate trips of ~ 18 days each (Prague Vienna Wassau Salzburg and Krakow Eger Budapest & onto to Croatia).

You should start either in Budapest or Krakow since they are on either end, north or south. Either Budapest, Prague, Krakow OR Krakow, Prague, Budapest. Any other order and you will be doing a lot of backtracking.
You can easily drive this but you'll have three issues, two big and one small.
1. Picking up a car in one country and dropping it off in another will incur very large fees since the car has to be taken back to it's country of origin. That's one reason so many opt for the train on multi-country itineraries that don't end in the same country in which they begin.
2. Some rental car companies will not allow you to take a rental car into the Czech Republic but this seems to be changing...check with the individual companies to see what their policy is.
3. You will also need to get vignette's to drive in the Czech Republic, Slovakia (you'll need to drive through part of Slovakia between Prague and Budapest), and Hungary. I'm not sure about Poland. These vignette's are easy to purchase at various places near the border crossings - just follow the signs. Some of these places only take cash so be prepared.
All that said, driving in these countries can be more difficult that you might think. The highways are in excellent condition but there can be a lot of truck traffic and road construction that will add to your estimated travel times. Once you get into the cities parking will add a significant cost plus you won't need the car at all while you are there.
Driving in these cities is doable but challenging. I've driven in Budapest and Prague, as well as many other big European cities, and it can be fairly difficult depending on where you are trying to go. If you are used to driving in big American cities it helps but you really can't compare it to a European city where streets are laid out in irregular patterns, are extremely narrow, with lots of one way streets. If you make a wrong turn you can't just go around the block. Parking garages are generally good but why pay for that when trains are so easy and public transportation is so good?

Usually when you are sticking to big cities, a rental car is usually not the best way to go. To paraphrase Rick, in big cities a car is an expensive headache. As someone else pointed out, you also would incur a large drop fee on the car rental. Krakow is an outlier which is a big part of the reason my wife and I have not made it there after fifteen Europe trips. I might be a little more worried about break-ins and theft in some of the countries you mentioned, too, than some places farther west (although France is known for break ins).

Looks like there is still a night train with sleeper cars from Krakow to Budapest (check bahn.de). We did a two week trip from Budapest to Prague in 2011 by train and bus, and got to see a lot of smaller cities like Sopron, Olomouc, Telc, and Cesky Krumlov. This included five nights in Budapest and four nights in Prague. With three weeks you could easily add Krakow with the overnight train mentioned above. Staying places along the way lets you break up the journey so you are not spenging six or seven hours getting places, too. Just my view, if after researching it you are still set on just these cities, then go for it.

Some people will say it's impossible to sleep on a train but my wife and I have found it's not bad and a lot easier than sleeping on a plane. These are far-flung cities to connect on one trip and once you begin to research it, you may find that some of the smaller cities and towns appeal to you for a one or two night stay, which with three weeks still would leave you with ample time in the bigger cities. I recommend picking up Rick Steves Eastern Europe.

Thanks so much for your thoughtful and courteous responses. We did just get Rick Steve's Eastern Europe guide and will be gathering more information from that too.
You've really had us stop and think about trains vs. car and the advantages. I do like James' idea about renting cars to travel out from the cities while taking trains into the countries.
Anita, your 3 points were definitely food for thought and discussion-starters today.
Thanks so much, everyone, for taking the time to answer and help.

My suggestion was based in part on the fact that you were set on renting a car. Do not hold the car while doing the city sightseeing. Parking in the cities you are going to is difficult and expensive.

If it is your first trip to the region understand that you can take a different day trip or overnight trip by train and not scratch the surface. I could give you 4 good trips out of Budapest by train. All of the at a fraction of the cost and hassle of renting a car.

For me the car would be for a particular goal and not sightseeing. We have used cars to go to the Slovakian mountains fly fishing for instance; and on Sunday we used a car to go about 2.5 hours south of Budapest to Mohacs for a festival. I said we used a car, but I didn't rent it, we hired a driver. It can be affordable in this part of the world. The 11 hour day was under 300 euro and there were 4 of us. I still would have done it had there been just two of us.