I actually asked the same thing here recently! I never posted the results I had from my search (mainly because they were so few).
So when you’re talking about learning a language, I have found that nothing really beats Middlebury language programs without getting out of the country (Correct me if I’m wrong anyone). It’s a complete immersion without being with people whose culture is vastly different (but you get to learn a lot about culture!). You aren’t allowed to say a single word in English while you’re there; only the target language.
Then there’s N-SLIY, or National Security Language Initiative for Youth, an actual immersion program (you go to another country). They do stuff for a lot of countries and languages you wouldn’t find in the average American or British (or any western) public school, like Tajiki, Hindi, and Persian.
The one that I’m applying to is called SLIYS, short for Summer LInguistics Institute for Youth Scholars. There, you can choose a language, and they assign you (or a group of students) a native speaker to help you learn and research the language. You also learn about linguistics as it applies to English and other languages (including your target language).
American Association of Teachers of German has Summer Seminars in Germany. I don’t really know much about them.
Besides those, NETC is an Educational Travel program that many schools go through for foreign language program Spring/Winter/Thanksgiving/Summer Break trips, but I don’t think you yourself as a student can do it; it would have to be through a teacher.
All of the above, except the German one, is for American students. I have no idea about anything regarding programs in other countries.
If you know of any others, please let me know!
I’ve got two more now!
There’s Concordia Language Villages, which is more for a younger crowd and slightly more focused on culture, from what I understand based on the information on their website.
STARTALK is like the little sibling of NSLI(-Y) that doesn’t require travel to a new country. It generally takes place at community colleges (and apparently you can get college credit for doing it) but keeps the general idea of immersion in mind. Apparently, they are supposed to announce the locations and application process some time this month!
I also forgot to mention that for those above 18, in college/university or beyond, there is the CoLang, a conference about collaborative language revival every two years (even years) (there is a workshop for a couple weeks on field work, then you actually start working for another few weeks; it’s over the summer).
Then the Linguistics Society of America puts on a meeting every year, and the Linguistics Institute, or Linguistitute every two years (odd years).
It turns out that many Universities have their own Summer Programs. Here’s an extremely non-exhaustive list:
Keep in mind that you might have to be an undergrad or grad student in order to attend some of these