Northern Italy and which other destinations - 2.5 weeks

Northerrn Italy, Western Tirol of Austria and Bavaria would be perfect for your family. The mountains are incredibly beautiful.
And Munich has so many interesting museums including the Deutsches Museum, the world's largest technology and science museum. The Munich Residence is the downtown palace, and it's also great. Nymphenburg Palace is also there as well as the BMW Museum. We took our daughter out to Dachau, and it did make quite an impression on her.

I would not do Spain in June - HOT!

My boys (12 & 15) loved the Salzburg area when we went in June 2018. Mountain coasters, salt mines, water parks, lakes, castles, gorgeous scenery, cute city.

The big fees from car rentals happen when you rent in one country and drop off in another. Avoid this by renting and dropping off in the same country. Then take the train between countries. Most large train stations have car rentals. You could tour northern Italy, drop off the rental car in Bolzano, train to Innsbruck (about 2 hrs). Pick up rental car, tour Austria. Drop off rental car, then train to Munich (about 2 hrs).

Or fly into Munich for 2 nights, pick up car
Salzburg 3 nights
Ljubljana 2 nights
Venice 2 nights
Milan 2 nights
Dolomites 2 nights
Garmisch partenkirchen 2 nights
Munich 2 nights

Plenty of water parks, mountain coasters, castles, museums, gorgeous scenery and great food for all!

Biggest caveat... we have to be able to fly direct from San Francisco and return to New York non-stop as well.

How can we give you ideas without knowing what cities are available? Please provide a list of those cities!

Thanks for the replies. David & Travel4Fun, I'm so glad you mentioned Austria/Bavarian Alps. Seems a pity not to go when we'll be so close. And thank you too for the transportation info. I have lots of research to do!

Chani, I wasn't expecting you to know which cities fly direct. I figured there'd be suggestions and I'd figure it out. But since you asked... :-)

Airport City
BCN Barcelona, ES
CDG Paris-De Gaulle, FR
FRA Frankfurt, DE
MUC Munich, DE
MXP Milan, IT
ORY Paris-Orly, FR

Thanks everyone!

you could fly into and out of MIlan. Head straight to Venice and spend 3-4 days there. Then pick up a car for a loop up to Munich through Austria ( Salzburg) and then back through Switzerland to MIlan for your flight home. Include one of the lakes ( Como, Maggiore, or Lugano) on your way back to MIlan. ( I don't know the driving routes so cannot suggest which one).

You would need to acquire the proper vignettes for driving in Austria and Switzerland.

I'd go with Barcelona or possibly Frankfurt. Barcelona has lots of everything. Frankfurt is smaller, quieter, and one of the most underrated cities in Europe, with interesting day trips, including Büdingen with a well -preserved medieval center and castle.

Your boys will probably be fed up with cities, so add a few days at lake Garda and visit https://www.gardaland.it/en/ and https://www.canevaworld.it/en/

Thank you to everyone who has replied. Your feedback has been very helpful.

Lola, I think flying in/out of Milan is a good suggestion. Certainly helps bring the airfare costs down. I'm now thinking:
Milan > Zurich > Munich > (poss. Salzburg & Ljubljana or straight to) > Venice > Bologna > Cinque Terre > Milan

I have yet to look into car rentals yet but it looks like it's a relatively short train ride between each of these cities.

Thanks again!

Remember that you can fly open jar- arrive in one city, and depart from another, usually for the same price as the RT flights, [my experiences.] Maybe substitute Lake Como, since its SO close to Milan, and skip crowded Cinque Terre?
Safe travels!

PS-
So maybe fly into Zurich and out of Milan, or reverse? You'll have a great adventure with your family!

Trains work really well for that, and you don't want one in Munich anyway.

You could rent one when you are ready to leave Salzburg and drive to Ljubljana and tour Slovenia for a few days ( highly recommended,). Return the car in Villach, Austria ( returning in Austria should avoid drop fees) and continue to Venice by train.

Between MIlan and Zurich, you could take the Gotthard Panorama Express, a train and boat combination between Lugano and Luzern.

https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/panoramareisen/gotthard-panorama-express.html

Lugano is a short trip from MIlan that you could do the day you land. And Luzern is a lovely lakeside town well worth an overnight.

I personally would not include Cinque Terre. It was overcrowded when we took our daughters there ten years ago, and has only gotten worse. If you want some beach time for your boys, there are good Lake options on your route, or Adriatic beaches closer to Venice.