Like many people, I have a lot of print journals that I got over time with association memberships. However, I never use them, given online access at my institution. Does anyone know where I can donate them? I've looked at a lot of university libraries and often, it doesn't look like they accept them, as a policy. Most of the online guidance that I have found is fairly old, at this point.
Most US institutions have subscriptions to the most important journals that include online access of past content -- so they will generally not have any interest in stocking yet more paper in their archives.
This is different for developing countries where space is less expensive than journal subscriptions. I've had colleagues will connections to third world universities to which they always took boxed of books donated by colleagues every time they went. I suspect that if you ask around enough, you'll find colleagues who know someone in Africa or Southeast Asia who would be interested in taking books and journals -- but you may have to pay for shipping.
I did this once - essentially, I had a bunch of print copies of a journal, and I asked the local university if they wanted them (along with some books). They said they could take the books, but had moved to electronic subscriptions for most journals.
I did however find United States Book Exchange (http://www.usbe.com) which, if you're in the US, is a non-profit repository of back issues of things, including journals, for libraries. They were able to take about half of the journal issues I offered, and reimbursed me for media-rate postage.
An off-the-wall idea is to ask colleagues in your department, at local community colleges, and in high school social studies/government classes whether they would like to use them for in-class activities. This might be good for early exposure to the idea of academic research, since many students don't start to engage with academic articles until later in college (instead just learning from textbooks).
For instance, each student could take home one journal and pick one article to summarize and present to the class. Or the students could mark the thesis statements, highlight interesting vocabulary words, note how citations are used, see how statistics are used and written up, etc. One of my professors did a helpful exercise where he cut up copies of the introduction of one of his own articles and challenged us in groups to rearrange the paragraphs, based on the logic of going from broad to narrow.
I could see these journals as being useful materials for the right instructor and the right set of students.