Foam core is awesome!! Another thing you can do with it is use it for mounting photos using drymount adhesive. Its like Heat n Bond for paper. It is usually used with a big press, but an iron will work, especially if it doesn't have steam vents.
If you want to give them to starving students, universities/ colleges with design or architecture or photography departments would probably be ecstatic to get some free foamcore boards, even if they are used on one side. Just make sure they have no dents, as that makes them ineligible for use in this application.
Giving them to a school that does a science fair would also be great, if they are still large enough to use for a presentation.
This makes me think I should call our huge convention center and see if they have a foamcore board reuse program. Thanks for triggering that great idea!!