First trip to Europe for 2 -17 year olds

Are you visiting your son during your two-week adventure? Have you purchased plane tickets yet? If so, where are you flying into and out of? What time do you fly home on departure day? How many nights will you be in Europe and this does not include the flight over.

A bit more information would be helpful as mentioned. And do you really mean Lichtenstein or do you mean Liechtenstein? Different places, but both are far from Budapest. And why are you considering renting a car if you think the train will be more economical?

Look at flying to Paris is my suggestion. And home from Budapest or Munich or Zürich, depending on where your son will be.

He will likely be in Eschen, Liechtenstein and he is hoping to join us when he can, likely on the weekend. We do not have airline tickets yet, but based on what I am finding for flights we will likely be arriving on a Saturday Morning if flying into Paris. We would be there for 14 nights. The dates we are considering are arriving on June 22nd and Flying home on July 6th. I meant to say driving would be less expensive and more flexible. Thank you!!

If you rent a car, you'll probably face an extraordinarily high drop-off charge if you pick it up and drop it off in different countries. Don't discount the possibility that a combination of trains and rental car may be best.

I've never rented a car in Europe, but others have reported challenges with trunk capacity for groups of 4 or 5. Be sure you can get a car that will accommodate your luggage as well as your people.

Lots to see and do in western France that is easy by car, but meeting up with your son might be tricky.

Just to give you a small list just in France:
Verdun
Nancy
Alsace (Strasbourg, Colmar, Mulhouse and surrounding area)
Belfort / Besancon / Salins les Bains / Champagnole
Lyons
Grenoble, Aix les Bains, Albertville, Mont Blanc
down to Nice, Monaco, Cannes
You can dip into Switzerland in this route and pass through Geneva

You should also check the route of the Tour de France because it might be either something you want to see or something you wish to fully avoid. Pre-Olympic buildup in Paris will be a beast to navigate near the end of your trip as well, so keep that in mind. I know in Atlanta, the city was crowded for weeks leading up to the Games. So maybe do Paris near the start.

Other options would be to head toward Zürich or Freiburg / Black Forest and then north toward Stuttgart and Heidelberg. Or north toward Lille, Bruges, Ghent, Brussels, and maybe Luxembourg and Trier.

All of these options are super fun with a car, more rural, and give a better picture of off-the-beaten-track Europe. But if you are Europe newbies, sticking to big cities might be the better option, in which case I would suggest Brussels (Bruges and Ghent can be done from there as ambitious day trips) or Munich in addition to Paris. Both have enough in and around them to be interesting after Paris, are easy to navigate if you don't want to be on the road a lot, and want more city Europe (more English, etc.) and are as accessible as anything else from Liechtenstein.

I appreciate all of these suggestions! Thank you for all of your feedback! If anything else comes to anyone's mind please continue to suggest.

Note that the Olympics are in Paris this summer. Are you finding air and hotel rates reasonable? This may influence your itinerary.
Have a great family trip! Safe travels!

I meant to say driving would be less expensive and more flexible.

Don't be so sure about that. Remember that the cost of renting a car is not the only cost of driving. You also need to pay for fuel, parking and tolls.

And price is not everything, travel time is also important. Paris to Zürich is four hours by train, or a seven hour drive.