Germany, Czech Republic, Austria & Hungary in 12 Days

That would be an ambitious schedule without the kids. With the kids, I suspect by the time you get home you will feel grateful you survived, more so than having pleasant memories of a family vacation.

I have not done the research, but I suspect Italy would not be hotter in any meaningful way than this itinerary in July

I suggest you cut Berlin as it's out of the way and is less scenic than the other cities. Also, Berlin isn't that clean and sometimes smells of beer and pee, depending on where you go.

Berlin, Prague, Vienna, and Budapest.

Sure, just depends on the pace you want to maintain. That's more or less 3 days a stop. More time than a lot of RS tours. Im not a big fan of Germany and would drop Berlin too, but if you love the idea, do it.

I can look up whats happening in Budapest in July. I would guess earlier in July would be better than later; Start in June if you could.

Not that it would matter much, if any, but you might start in the south (Budapest) and work north.

If heading north to south, from Prague I would fly to Budapest, then train to Vienna. But look at all the options for the best Open Jaw ticket.

Given the uncertainty and ever-changing covid mandates, four countries is just too much. Do some research regarding what it takes to enter countries currently: countries' trackers forms, airline forms, covid testing, vaccination mandates, times four people, et al. I actually did go to Switerland Sept, 2021, when we all THOUGHT covid might wain, had a great trip, but spent significant amount of time on the prep work. Then, once we left, mandates changed again, and we only had one country. Spend some time researching here on the Forum under the various nations, to get a feel for what folks have had to do who have been traveling. My advise is to chose two countries , at most, and have a back-up plan if you need to change the itinerary at the last minute.

Is it twelve days on the ground in Europe or twelve days total?

Good luck!

Berlin isn't a quick stopover. Independent travelers to Berlin should probably plan on 4 days of sightseeing. But with kids along, I would think an extra couple of days would be wise; consider an outing to (or a stay in) nearby Potsdam + some recreational time in the area (Wannsee?) The Bridge of Spies (Gleinicke Bridge) and Pfauneninsel (nature preserve) are there too.

Berlin (5-6 nights) + Prague (3-4 nights) + Vienna (3-4 nights) would be rushed but possibly doable with an "open-jaw" flight using Berlin and Vienna airports - and a tightly-structured itinerary. These cities are separated by roughly 4.5 hours of train travel. I would probably arrange train journeys between cities in the late afternoon (like 15:30 > 20:00, for example) and have dinner on the train (either in the Bordrestaurant, where it's often tricky to find even 1-2 seats, or out of your own picnic sack with self-selected take-out items) on those two days. You're likely to be much happier with food and drink you can pick up in/near the stations.

I would not attempt Budapest on top of that.

My opinion: 4 cities in 12 days(assuming you mean 13 nights) is too rushed for 2 adults let alone with 2 kids.
Coming from experience I would suggest you cut it down to 3 max.
Plan on arriving in your first city and departing from your last city to minimize travel time.
I usually have travel in July and just deal with the hot weather if it shows up.

It’s important to know how many nights you will have in Europe. I plan by how many nights I have in each location to determine how much time I really have. Two nights = 1 day, 3 nights = 2 days, etc. You can’t count your arrival day as you won’t be able to see much and your departure day will be getting to the airport as you will likely have a morning flight. As for transiting from one city/country to another you have to factor in not just how long the train ride is, but also the time it takes to pack, get to the train station and wait for the train. Once you reach your destination you have to get to your hotel, check in, etc. You have to figure you will lose a half day or more each time you do this. It’s a lot harder to move fast with kids as well. Assuming you have 12 actual nights on the ground you will have 11 full days to work with. I agree with dropping one city. Geographically it looks like Berlin is the most out of the way. If you must go to Berlin I would drop Budapest as the other city that would be most out of the way. With 3 cities you would have 4 nights in each, so 3 days to explore. Definitely fly into your first city and home from your last. Search multi city when looking at flights.

Have you thought about substituting Munich for Berlin? I think your kids would enjoy Munich more, and it's much closer to Vienna than Berlin is. You could then head to Budapest, which is also not too far (relatively speaking). But as others have mentioned, I would keep it to 3 cities, rather than 4. You will be very stressed and rushed.

Plus if you are able to stay an extra day in each city, there are wonderful day trips available. From Munich, Rothenburg o.d. Tauber or Dachau (2 very different trips but both worth visiting) are close by. You could stop in Salzburg on the way to Vienna, or take an afternoon river cruise on the Danube to Durnstein (a lovely and charming village). Day trips are really nice to build into a trip because it can get you out of the city for a bit of relaxing and beautiful scenery.

You didn't mention transportation - are you planning to take trains or rent a car? Hopefully trains - cars are difficult if not impossible to drive around European cities. The few times I was forced to do so, it caused me an incredible amount of stress. Trains are easy, fun (you can watch scenery instead of paying attention to driving) and relatively inexpensive as long as you buy them far enough in advance.

Which cities, and for how long is a personal preference thing. So, I will skip that other than to say that a fairly full tour of each is probably 3 to 4 full days. But who said you can't just hit the high spots and return some day if you liked it. My first trip to Budapest was 2 full days. Now I have been back maybe 50 times. My first trip to Vienna was scheduled to be 5 full days, I left after 2 because Vienna just wasn't what I had hoped. But I would not have known if I hadn't tried.

Given the uncertainty and ever-changing covid mandates, four countries
is just too much.

Naaaa, I did 6 countries in August last year. No big deal and its not any harder now. And don't come here for advice, because opinion isn't what you need, you need facts so go to the official site for each country. My guess is you will have little trouble traveling between EU countries. But do the research, then go enjoy.

@Nestor: Hi, haven't seen you on the Germany forum for a while. Hope you'll be back soon to share more impressions, experiences, and your usual thoughtful comments here...

@kmardalan: Munich is a viable and popular destination, not necessarily my top pick for Germany, but as Mardee has suggested, it can also serve as a good travel base for certain day trip destinations. The same is true for many other cities too.

Mardee's "home base + outing" tactic is often a good travel strategy for families, one that I generally support. You get to see more places - usually smaller places - in less time and without the need to be packing/unpacking and transferring yourselves and all your stuff on a strict timetable as you move from place to place. With only two base towns, you'd have only one base-town move to make. You'll still have deadlines, but you'll be less likely to lose possessions, and your kids will probably feel a bit more "at home" wherever they are. From Berlin, for example, day trips to Sachsenhausen, Lutherstadt-Wittenberg, or possibly Dresden, could be on the table. Perhaps you could find and do similar day trips from one of the other cities you've listed as well, or drop Berlin and do some other 2-base-city combo.

You would need to make sure that your accommodations are fairly near the main station or travel hub for efficient outings. And do check out these day trips very carefully, including train travel times and frequency on your own before assuming anything - what might be acceptable/enjoyable to someone on this forum might not work for you at all. Some parents would not want to take young kids to a Holocaust memorial site like Dachau (which btw specifically advises parents not to bring young kids along) or Sachsenhausen (the one near Berlin.) And what might be an acceptable travel time to one person (like 4 hours round trip on the train from Berlin > Dresden, or 6 hours round trip from Munich > Rothenburg) might seem like a bad idea altogether to others.