I had three monitors we didn't need anymore. I called local thrift shops, local shelters, asked my son's ST, neighbors, ads in Freecycle and Craig's List, and I even set them on my driveway with a "FREE" sign on them and NO ONE wanted a free monitor. One was fairly new too.
When our old monitor broke I would have been thrilled to find a free monitor!
I took them to my local solid waste to drop them off on the e-scrap pallet. When it's full they take them to a computer recycler about 2 hours away to disassemble them and recycle it.