College in the US $$$$ vs Europe where it's free?

No, but I am British so I would definitely consider sending my kids back to England for university if they wanted to. Currently the highest fees are 9,000 gbp a year (about $13,500, but less at the moment because of Brexit!). If you aren't a citizen though your kids will have to pay international fees, which will probably be substantially higher. I doubt there are other countries in Europe that will college educate a non-resident/non-citizen for free but I might be wrong. 

I have *heard* that tuition in Germany is free. I do know of a friend's daughter, from Oakland, who attended undergrad in London ( not free, but less than tuition here) who now is in grad school in Gerrmany, where tuition is free.
It is my understanding that classes in the universities in Amsterdam and Copenhagen are taught in English, but I don't know about tuition for international students.
My own daughter attends college in Canada, and I know several other kids who did the same. There are thousands of students from the US at her university. We pay international tuition; comparable to tuition at a UC. Canadian citizens do pay far less. We're very satisfied!
I believe that students who spend 4 years at a Canadian uni and graduate are eligible fora three year Canadian work permit; that can open the door to Canadian citizenship... an appealing perk in this election cycle.

Michael Moore's film Where to Invade Next, talked about free college in Slovenia, even for Americans. I see an article in the Wahington Post about places that have free college, with different caveats. https://www.washingtonpost.com/news/worldviews/wp/2014/10/29/7-countrie…

OMG, think carefully, especially when it's a freshman. Apart from tuition that, depending on the country, may or may not be all that low (ditto cost of living), there are other expenses, mostly travel: going there with your kid to check out schools, going there with your kid to get kid settled, getting kid home for winter break, etc. University abroad can be an expensive and time-consuming project. (I speak from experience; It cost us just as much as U.C. Davis would have and was far less convenient.)

Not that you asked us, but I think an 18-year-old, however smart and well-behaved, is too young to go overseas to university unless there are trustworthy friends or relatives around who've sworn to look out for her/him, or a dormitory system that provides some structure. (Again, I am speaking from experience; my husband's family were well-meaning but too busy to see much of our daughter.)

If you do decide on a university abroad, speak IN PERSON with parents who've also sent their children to that school; don't depend solely on Web sites and charming brochures and university employees. Sorry to be so discouraging, but the university-abroad experience has changed a lot since I did it as a 21-year-old. Good luck.

I second the advice of one of the posters to consider Canada.  Our daughter has been a student at McGill University in Montreal and has found it to be a wonderful experience.  There are a few other students from surrounding highschools at McGill, and she knows many others attending other Canadian institutions.  She has really enjoyed being the "international" student among many of her peers and has gained a different perspective on her home now that she is on the outside looking in. Learning about the culture and politics of another country has contributed to her overall education. The cost is comparable to a UC.  And, the cost of living is relatively low.  Certainly in Montreal.  She would definitely encourage students heading to college to consider another country.  Great experience, something different. 

Yes, I agree on considering Canada. My daughter will start at McGill in Montreal this fall. The tuition for international students is comparable to a UC, the cost of living in Montreal is quite low, and travel to Montreal is comparable to flying to NYC in terms of cost and distance. I am still amazed at how low the overall fees will be. The only downside is the winter weather, which is quite severe, but she is excited to learn about a new culture without being too far away from home. 

My cousin is getting her masters in Germany. It is free but she said she had to pass a written test in German.

There are school in Holland, like University College Utrecht and University College Amsterdam, where instruction is in English. You can Google them. With a European passport tuition is around $3 K, for Internationals about $10 K a year. These are excellent liberal arts colleges with small classes. Amsterdam is a bit crazy, for my taste, but Utrecht is a quintessential student city.