Teens' first trip to Europe - your reccs? :)

If I were in your shoes, I would be looking at a second destination within France, or possibly in a neighboring country easily accessible by train. I would definitely not lose all that time in transit to get to a second spot. It could take the better part of a day, and you just don’t have that this time.
France is certainly full of WW2 sites and maybe someone can give you a brief sampling, as summer is the only time I would want to go the northern coast.
If you want the more Mediterranean experience, you can head to southern France, where you can hike without thousands of others like you will at Cinque Terre.

Welcome to the forum.

Sounds like a nice trip idea.

First be informed that with age of 20 your "kid" is an adult in most European countries.

Europe offers many outdoorsy opportunities, e. g. the Alps which would lead to a first recommendation, e. g. Salzburg (Autria) and Berchtesgaden (Germany). Close to Berchtesgaden you will also find WWII related Eagles Nest, the mountain yard of #1 Nazi.

Another Alps option is Switzerland and of course the French part of the Alps, e. g. Geneva, Annecy, ...

Norway and Sweden are excellent destinations for outdoor lovers, e. g. Bergen and Western Fjords. Close to Bergen a museum hosts a wreck of an airplane from WWII and you will find some defense bunkers along the coastline. Very special for your travel time is far in the North of Norway the Midnight Sun, e. g. on Lofoten islands which will offer also beautiful beaches - with a little different temperature than Hawaii.

My few cents so far. More details available, also in the Country forums.

Ok, my first thought was Switzerland or Austria/Bavaria Germany. But then you threw in Paris...yay another favorite!
I would do Paris, then take the train to the Normandy & Brittany regions (base yourself in Bayeux and maybe one other place in Brittany. Rent a car for this part of the trip and take in the WW2 sites and the scenic regions and beaches, which aren't warm Hawaii beaches. (Very easy to drive in France except Paris.) Either spend the entire time in that part of France...You would be losing a lot of time going from Paris to the Greek islands. I think you should focus on one specific area. Ten days isn't really very long for changing countries.

Or Paris and someplace in the south of France. But with your son being so interested in WW2, you are so close, you shouldn't miss Normandy.

Ours were the exact age when we first took them...we did London and Paris. It was a fun family trip. They are world travelers now.
Enjoy no matter where you decide!

London ( reserve the Churchill War Rooms and spend 1/2 a day at Bletchley Park. ) Board the Eurostar to Paris. See Paris then fly to Venice. Nothing in the world like Venice.

You are traveling at the height of tourist season in Europe. Aren’t going to escape crowds anywhere. Remember Europeans also vacation.

You could also choose one country to explore.
Fly into Rome, train around Italy, arrive in Florence. Then train to Venice.

Or Fly into London, explore for 2 days then train York or Durham . Explore then head to Edinburgh or Glasgow.

Or fly to Dublin, rent a car and drive to Dingle by going over the Sally Gap to Cork and along the coast to Dingle

Or visit 2 countries visiting Eire and N Ireland.

I agree that you need to be looking at areas closer to Paris for what is already a short trip. And count your stays in nights rather than days. 3 nights is only 2 1/2 days of sightseeing. Don't forget that your arrival day will be affected by fatigue and jet lag, and every time you change locations you will lose a half to a full day of sightseeing. The Normandy coast or the south of France would be good choices. I'd recommend digging into some guidebooks or travel websites. Make a list of all the things your family would like to do in each place. Get the kids involved in this. That will help determine how much time you need to devote to each location. Finally, if you decide on Paris and the south of France, buy multicity flight tickets into Paris and home from Nice or Marseille to avoid wasting time backtracking.

The Swiss beaches are not that good. I would look at the Greek Islands if you want refined or the beaches of Montenegro if you want natural and lower cost. Or Croatia if you want expensive and trendy.

Our daughter absolutely wants to see Paris so we're thinking three-ish
days there. We're not the type of people who need to see everything -
If we don't check off the main tourist sites were OK with that - just
trying to absorb the culture and vibe.

It sounds like you've got the right attitude to avoid making Paris merely a "checklist" visit. You may already be thinking along these lines, but with only three days, if you and your daughter do not really have any real personal need to see anything in the Louvre or similar major site, you could skip it (that could save you an entire afternoon) and instead check out some of the small, charming museums and churches that most people miss but have art just as good.

I just love walking around Paris, exploring everything on foot and often just discovering things as well as getting a sense of the city layout and neighborhoods from walking around it, and that sounds like a good fit if you're hikers.

I've been to Cinque Terre twice, but only way back when Rick Steves just started talking about it; back then it really was special. The thing about finding that kind of experience today is that there are A LOT of other scenic little cliff villages and hiking trails along the coast you could also explore that have similar charm and sea views, are not so jam packed with tourists, and where the lodgings are still owned by locals. Some are just a few miles north or south of the Cinque Terre.

our daughter wants beach time (although she gets that European beaches
are not the perfect Sandy beaches that she's used to from Hawaii.)

I've spent afternoons on a beach that was huge, sandy, and mostly empty on an island just outside Tavira, Portugal (yes, I heard of the place because of Rick). So maybe the Algarve is one place to look, although perhaps not in the most touristy towns.

One crazy thing Paris does in the summer is pour a lot of sand along a stretch of the Seine to make an urban beach (Paris Plages). But I think it starts in July. That would not be what you're looking for, it's just a curious and fun thing that they do.

Our son loves World War II history but not quite sure how to weave that in

Well of course you already know there's Normandy if it fits the itinerary. I do like that part of France. I have a similar fascination about WWII but not enough that I change my itinerary for it. It's more like I notice when a place I happen to be in has WWII significance because of a museum, memorial, or plaque in town. Based on that, here's one idea:

Once you start locking down your major destinations, have your son research what happened at or near those places in WWII. Given that you'll be in France, Italy, and maybe Greece, there's a pretty good chance something happened in WWII near wherever you're going to be, whether it's a battlefield, a former military installation or airfield that is now a museum with artifacts like vehicles and airplanes, a former artillery installation on a seaside cliff that now gives tours of their underground bunkers, etc.

Given that your family likes the outdoors, you could for example research and plan a day out in some semi-rural area that involves walking down scenic trails that pass a WWII site.

I just did a quick web search and apparently in Paris alone, there are more WWII museums and memorials than you can ever fit into a 3-day visit...

The easiest solution would indeed be somewhere in northern France, Normandy being an obvious one (some beaches do not have bunkers). French people go there for beach time - but it is definitely not the Caribbean, more Long Island. Similar would be Netherlands or Belgium.
For a real full swim-and-subbed summer beach experience, you will have to fly from Paris - and there you are pretty free to choose. Some places have long and sandy beaches, actually - just the tropical feel of Hawaii might be missing, since the vegetation will be drier, coarser, and the water likely cooler in June than in August (when it frequently could compete with Hawaii)
Should you also want to do WW2 at the same time, you are probably best served with Italy or Greece - but I must confess, I do not know if they have any sites comparable to Normandy.

An example of seeing subtle evidence of WWII: While walking in towns in northern Italy, among the historical plaques that you often find on old building walls, we came across several that memorialized an Italian Resistance fighter from their village, called the partigiani (partisans) who are considered town heroes because they fought for liberation from the WWII fascists (Mussolini then Hitler).

So maybe that's another angle: Encourage your son to research what happened to the local populations during WWII in ways that would show up along your route. As a boy and young man I was of course more into the big battles and the military hardware, and while I still appreciate that, as an adult I think a lot more about how so many people were forced to suffer and how much of European history was sadly and unnecessarily destroyed because of that war.

On the one hand I am proud that my home town built a lot of Boeing B-17 bombers that helped win the war, but at the same time I can be in Europe reading about a historical district that was where I stand but I'll never see it because it was violently bombed out of existence probably by those same aircraft, so now it's a boring office building or mall.

Which brings to mind another example: He should keep in mind the difference between the towns that were relatively untouched by WWII and those that were almost completely destroyed. For example, one reason there are so many ugly modern areas in European city centers is because those areas were flattened by aerial bombardment, and when they rebuilt, it was in 1950s mid-century style that was absolutely charmless compared to what was there for hundreds of years before.

And also he should appreciate how some towns went to the great effort of rebuilding their destroyed historical centers as they were before, which tourists don't always know or appreciate...that the charming "old" buildings they are photographing and posting on Instagram are 20th century reconstructions of what was destroyed during WWII.

Deb,
It appears you have 8-10 days. Does that include arrival and departure days? If not, great. I would still stay in one country for that amount of time, as you will lose a day moving from Paris to your next stop, particularly iof you go as far as Greece or Italy or Croatia. Three days in Paris is 4 nights, Day 5 move, days 6 through 8, 9 or 10 in new location.
Day 1...arrival, sleep in Paris
Days 2,3,4...Paris, sleep in Paris
Day 5 move to ?, sleep in new place
Day 6,7,8,9 new place, sleep in new place
Day 10 depart If you have more time, add on here or move to location of flight home to sleep there the night before flight
If your total days are 8, then trim from Paris (a shame to do so IMO) or new place

The suggestions to stay in France or parts of Europe closer to Paris are good ones. Maybe Amsterdam? Re WWII sites and memorabilia, everywhere in most of Europe will have places to visit and things to see. Beaches, the Belgians and Dutch do go to beaches in their respective countries, and they have some nice ones. They won't be like Hawaii or So.Californis beaches, but your daughter will probably enjoy them.
Mainly, I believe with your limited time a far-flung second location would cut into your enjoyment.
Whatever you decide, enjoy!