July or August

Where in Europe?

Google the school dates for the countries you are considering. You may find some dates when the schools in the countries you are visiting are still in session. Not that people from other countries don't travel to your destinations, but it might give you some ideas for dates that seem to have the most kids still in school. I think I've used this website in the past, not for summer, but you can see the type of info available. I've found this approach quite helpful when picking my travel dates. Note that German schools have different holidays by state. https://www.holidays-info.com/germany/school-holidays. Similar info is available for other countries.

Can you start your trip in late June? Many of the European schools are still in session then. We noticed a huge difference in Copenhagen crowd numbers between the last week in June and the second week in July during our just-returned-from visit to Scandinavia. I don't generally travel in the summer, but I have noticed this trend in past years.

No one can truly predict the weather. Now with the reality of global warming that reality is especially true.

I haven’t traveled to Europe during the Summer months in decades. My preference is the fall because I live in LA. Some will think I’m crazy but sunshine and good weather 365 is BORING!

So in answer to your question I’d opt for late August.

No science or experience to back up my response.

I’m cranky. At present (1:23 PM PST ) it is 90 degrees outside. Yuck!

I know that pretty every place I've lived, the second half of August usually starts cooling down. Of course, you can't predict the weather as you know, but if push comes to shove, I'd say your odds are better then. :)

Also, many schools are starting earlier now; I know in my hometown of Cincinnati, many schools are starting around the 2nd and 3rd week of August, which means that many people will be done vacationing by then, so it might be a bit less crowded.

August is a popular month for Europeans to be on vacation. That means some shops and restaurants may be closed. You’ll also be dealing with local and foreign tourist crowds.

I would (and have) travel with my teens as soon as school gets out. For us, this is mid-June. The crowds increase as you get into July, as do the temperatures. I would not count on August being any better. You can look at historic temps where you plan to go. If heat is a problem (as it is for me), make sure your lodging has ac in all the bedrooms. It is not common everywhere.

Much depends on where you want to go. July in the alps comes with a lot of rain. August, yikes I can't even think about that unless your very far north. The later part of August in Switzerland would be best as far as I concerned.
I pulled my two daughters out of school (8th and 9th grade) for 5 weeks to go to the south Pacific. All the teachers had to approve the absence or they would fail. Most teachers were thrilled, the two stick in the muds were the choir and P.E. teachers, as if the world stops spinning with those to subjects. We argued we shamed and eventually got permission. The 9th grade Alberga teacher stayed late to keep her up with the class. The 9th grade choir teacher had her to do a hula dance (apparently she didn't know that only men dance in the South Pacific) she danced and kept her grade up. The choir classed missed out on what would have been some very interesting facts if she had just let my daughter do a presentation. The 8th grade English teacher had her do a presentation about the trip, she took flowers to school and showed the class how to weave the petals together for newnus (what we would call a fancy lay) along with talking about the differences in the cultures. Years later I asked my son if I could pull my grandson out of school for a trip, his response was that my grandson would learn more in one day with me that he would in the whole school year. Both of the girls are in their 40's now they both remember what they learned overseas much more that what they might have learned in 5 weeks of school. I say all this to tell you don't feel guilty if you decide to pull your kids out of school, take heart they will learn more with you and you won't have to have a boiling hot vacation trip. J

yes, I know, the heat

FWIW: Plenty of down jackets worn in Prague today.

August is better for big cities like Paris because locals leave for vacation. If you don’t like crowds go somewhere you haven’t heard of.

"Europe" is a bit larger than the continental US.

How much time do you have?

I always go in the summer, regardless of the crowds and the heat. True, the heat can be oppressive and stifling, have experienced heat waves in July and August. You deal with it or work around it. The crowds don't serve as a deterrent if I am determined to see a popular site, as they are likewise determined to do.

To answer your question, my choice is July for several reasons.

Well, so far August in Budapest the daily highs have ranged from 68F to 84F. Mostly in the mid to high 70's. I'm not suffering. August, in this one location, is across the board cooler than July.

In Rome, for example, the temperature drops from 89F early in the month to 87F by August 21. So yeah it really cools down later in the month.

Thanks for the information everyone. Much appreciated!

I was checking the weather for Florence Italy this week and it was over 100 degrees, so the end of August theory being cooler may not happen. I know a lot of families in your situation and I would start vacation as soon as you can in the summer, even the day after they get out of school, which for us is mid -June. The great thing about Summer travel is you can sleep in a bit and really enjoy those long Summer days where it does not get dark until 9 or 10PM, so you can go at a slower pace and take more rests.