If you are part of any larger groups, IRL or online (like a church group, a parenting group or a workplace whose culture would allow it), I would start mentioning that I have surplus to give away...especially if there are group members who are younger or just starting out. When I was just out of grad school, I ended up with a couch, a full set of dishes and a whole wardrobe of nice shoes from people who were downsizing and delighted to have someone take their things. Plus it makes it ok to discuss such things in the group culture.
I have also done well by putting things out in a group space (like the work kitchenette) with a sign "free to a good home." People who might be too shy to ask for things will take them. I used to live in a neighborhood where you could get rid of anything with a "free" sign. Unfortunately that is not allowed in my current 'hood...
