Emily - You may want to try your local churches -- many have members who are deployed or who have family members deployed. I also second the information about trying your local National Guard office and the previously mentioned veterans groups.
In addition to "anysoldier.com" I would recommend
http://booksforsoldiers.com/-- this last one is a forum where military members can post request for specific items and provide their addresses.
Operational security dictates that only the service member can give out their address - meaning that no one else can give it out for them without their permission. In the world of letter bombs and anthrax in envelopes, writing soldiers who are deployed has gotten a lot more difficult.
It is also possible, with a little research, to find the address of specific units who are deployed to the war zone. Check the newspaper or news reports for unit identities, then do a web search for the unit web page. There will usually be a general information address (usually the Chaplain or pulic affairs officer). They have programs to deliver mail to Soldiers who may need it.
Another option would be to contact your local Veterans Administration Hospital and see if you can do something for the men and women there. These veterans are frequently overlooked and need some help in their long road to recovery, and every positive letter or card helps -- visits help even more.
Good luck with your project.