I am a graphic designer.
I definitely agree with the responder who said theater helps, because it gives you a chance to really use graphic design skills (advertising, designing the program, etc.) The school newspaper or yearbook would also be excellent opportunities.
I think you can also find other opportunities to help out with just about any organization (church, school, etc.) -- "Hey! I'll design a flyer about that!" or "Let me do a display about that at the open house." -- there are design opportunities, even if that's not what the club/activity is about.
As an example, I was in 4-H as middle/high-schooler. Although 4-H isn't focussed on design, there were a variety of projects that a person could take on that use graphic design skills. I competed at the state-level in public speaking (with visual aids). I did a photography project every year. I always volunteered to be in charge of designing the booth to showcase our 4-H Club at the county fair. (I also raised rabbits and did some sewing and cooking projects -- more traditional 4-H stuff -- but the opportunities are there for design, too.)
Graphic design is really about communication and problem-solving though... so I think any time you do an activity where you have to think "How will my audience perceive this? What message will they take away? Am I communicating what I want to communicate?" you can get some experience that will be useful (photography, dance, music, etc.) Those aren't *directly* related to graphic design, but you have to think in the same way.