European destination 10 day’s end of May?

You will probably find crowds just about anywhere/everywhere at that time.

"Overwhelming" is subjective, like the ideal shower water temperature.

You would certainly be there before the summer max crush.

I do not think the crowds will be overwhelming at the end of May. Italy is always going to be busy because it’s a lovely spot that many people want to visit. We were actually there in mid-July last year and it was not as crowded as I had feared. It is definitely crowded, but is not unmanageable. Do as you like and take your trip. Make sure to read Rick’s books about Italy because he has excellent tips for skipping the lines and making the most of your limited time.

We've spent more that 600 days as EU tourists, and we are less than impressed with Paris, Florence, and Vienna. Ponder these: 1] Prague, Vienna, Budapest. Italian food is surprisingly bad unless you spend big bucks. In the former Austrian Empire, the food is weird, but fascinating (French Fries and KFC originated in Vienna) and the dark beer is to die for.

Second, Elba River Cruise from Berlin to Prague. This is sort of off the beaten path, partly because it is mostly behind the Iron Curtain. Its very relaxing because (at least when we did it) there was no night travel on the Elbe, so the boat days went like this: half a day sight seeing, half a day travel, but we spent travel time on the sun deck watching the scenery go by.
I don't recall the length of the Elba trip, but if you have any extra days, spend them in Prague.

There is a reason why Prague is on both. Its the top city to see in the world. Stunning architecture, even beating Barcelona. Weird food (try garlic soup), & great, cheap dark beer.

Third, The best 3-5 days you can spend in Europe is in Alsace. The next best 2-3 days you can spend in Europe is the Mosel Valley, and the two are easily connected, BUT, you have to have a car. Round out the trip with Heidelberg, Mainz Bad Wimpfen etc.
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Don't let the crowds scare you away from the BIG 3 in Italy. That trio is fantastic and great for 10 days.

Do an open jaw ticket into Venice or Rome and take the train to Florence ending in the other city.

We were there in June of last year (Rome and Venice) and the crowds didn’t feel overwhelming. As Rick mentions in his books and shows, step a little away from the main drag and the streets seem to empty out, even in Venice. As others have mentioned, pre-booking major attractions also helps with that feeling a lot. If that’s where you want to go, do it. A little planning and research will go a long way to helping to alleviate crowd frustration and you’ll have a wonderful time. I’m Venice, it helps to stay in the city and plan to go to some of the bigger sites either first thing in the morning or later evening, to avoid the cruise ship crowds. Spend the mid part of the day relaxing and exploring back streets. I was surprised at how friendly and welcoming the people in Rome were, given how big a city it is.

Crowds are a fact of life in Italy, if it's not people from other parts of the world, it's Italian's themselves trying to see the sights of their own country. Plan to see certain sights either early in the morning or, late in the afternoon or, evening. In Venice keep aware of the cruise ship schedule and you'll notice a drop in crowd density as the day gets late. Same thing in Rome, if you hit Trevi fountain or, Spanish Steps mid-day, standby for combat-tourism. Peak around the corner of those sight and you'll see brigade of tour buses waiting for their passengers.
May shouldn't be too bad, weather will be quite pleasant and the crowd intensity will be, manageable. Fly into Venice, train to Florence & Rome, fly back from Rome.

Thank you everyone for your input & ideas!

In response to some of your questions our daughter has been to Spain with school and is currently in Guatemala with our church. We have taken her to Mexico & Jamaica but neither of those were cultural experiences since we were at a resort. My husband & I have been to Rome & Paris but always in April when weather is not ideal but crowds are down.

After all your responses I am more confident in Italy but will also consider Germany area. In the end I will let ticket prices and her interests decide where we go.

Any other suggestions will be appreciated. This is a great resource and group of people!