I was on Facebook, and noticed a post from Plastic Pollution Coalition talking about a program by D'Addario and Terracycle to recycle strings from musical instruments. The timing was perfect, because I was just about to replace the top two strings on my cello.
You can find a limited number of local events held by music stores here, or D'Addario will send you a free shipping label so you can send them your strings to recycle. All you need to do is sign up on their website. Once you're signed in, just click on "recycle" at the top of the page. You can earn points for sending in strings for recycling, either to use to buy D'Addario strings, or if you don't use that brand, you can use the points to go towards helping school music programs. If you teach in a school, or if you have a music store, you can also send a request for a collection bin.
I was so excited to find out about this program! Strings don't last forever (for me, no more than 6 months to a year before they stop responding well), and I've always been stuck throwing them in the trash. So glad there is finally a solution!