With only 9 nights you should stick with Prague and Budapest. That is still a limited time to see all of the major sights in each city. It would be more productive to do a day trip from each of these cities and really get a feeling at least for the capitals of two countries than to rush around through three.

Having spent 6 nights in each Krakow and Prague (most recently to Krakow this past spring with our 10 and 15 year olds), I would propose flying into one of those cities and out of the other, and saving Budapest for a combination Vienna-Budapest holiday later if you're so inclined. From Krakow you can day trip to Auschwitz and the salt mines; and from Prague you can day trip to Kutna Hora and Theresienstadt or make a long day (but preferably an overnight) to Cesky Krumlov.

We recently made a long day trip to Budapest from Vienna, our only purpose being to see the castle area. Budapest seems to warrant an additional day or so, but we thought four would be too long.

fourfortravel - how did you travel between Prague and Krakow?

Were your kids allowed to eat and drink with you at all establishements?

In 2003, we took the train from Prague to Krakow. We traveled during the day to Krakow, and took the overnight train from Krakow back to Prague. We had to return to Prague because we were with our daughter who was studying in Prague at the time.

So you could fly into Prague, take the train to Krakow, and fly home from Krakow, if you choose those two cities. I would recommend staying overnight in Cesky Krumlov for one night rather than doing a day trip. It's a beautiful city & we especially loved it at night.

I would not do three cities in 9 nights with a kid in tow. Prague > Budapest > Krakow.

We stayed four nights in Budapest and six in Prague and needed more time in each. For some daft reason Budapest gets short shrift on this board and Krakow gets much love, but from a historical, cultural and political perspective, Budapest is well worth the time. The Hungarians trace their lineage far differently than Poles and Czechs - Magyars are closer to Finns and Estonians and are NOT Slavic like Czechs and Poles.

Better to answer this: why Budapest, Prague and Krakow other than "well, they're there"? For WWII history, none have much importance - the Nazis didn't annihilate Krakow like they did Warsaw; the Czechs were sacrificed at Munich and Hungary's government cooperated with the Nazis until 1944 when the Nazis just took over.

From a Holocaust perspective, Krakow is near Oswiecim and has the Schindler sites and that could be rough on a 12-year old; Prague is near Thieresenstadt (Terezin), which was actually rougher on me and my wife than Oswiecim (which is more museum-like), although Birkenau was horrific; and Budapest has its Dohany Street Ghetto including the Weeping Willow. Hungary had the second-highest total of Jews killed in the Holocaust (Poland, by far, topped the list) even though the Holocaust didn't reach Hungary until 1944.

From a Communism perspective, Budapest has more interesting places than the others (Szoborpark, Terror Museum, information on the 1956 uprising) although Krakow has Nowa Huta and the Arka Pana - both of which are worth a visit and both of which are outside central Krakow and therefore you may miss it in a 3-day trip. Despite both the Velvet Revolution and the Prague Spring, the Czechs seem far less resentful of being under the Soviet lash than either the Magyars (one number: 1956) or the Poles (two words: Gdansk Shipyards).

From an architectural perspective, they're all pretty much fish-in-a-barrel although (1) Prague Castle > Wawel > Buda Castle; (2) Charles Bridge > Chain Bridge > any in Krakow; (3) Hungarian Parliament > Czech Parliament (no equivalent in Krakow).

Note that in the post above I'm merely separating the Holocaust from broader WWII history (i.e., Gdansk is the site of the first fighting of the war, Warsaw was overrun by the Russians and Germans).

We were in Krakow in 2012 and in Budapest in 2005. You might be interested in my trip reports; click on my name to find them.

I agree with those that say to do only two places and not three.

Too much to see in Prague and Budapest and you are travelling with a 12 year old.
This will "slow" you down a bit. You want to tour at a nice pace not rush, rush because you want to see city number 3.

There is an overnight train between Budapest and Prague if that helps?