What are the most effective/interesting places to volunteer, in the industry of project management?
I'd point co-organizing a local conference or other community event. Conferences like TEDx can be pretty big (like 500 people) and there's always a need to for help. You can learn a lot about leading projects there. However remember about voluntary project specifics. See: What can I do to prepare for managing a project which is staffed mostly with volunteers, for a non-for-profit organization?
Another idea is organizing some event, i.e. holidays, for your friends. If you approach this task thinking about it as a project you can learn pretty much. Especially that friends make pretty difficult clients - often you can't count on their discipline and you don't want to play hard balls against them (something you'd consider against clients).