No to the landfill. Put it in a donation bin for an organization you support, or check for local organizations that do textile recycling events (we had one recently done by the Scouts, and another by the schools). Textile recycling is great because they reuse all kinds of fabrics including things with rips and stains, and things like shoes, belts and purses.
I have a friend who runs a rag business, and he collects unusable stuff from the charities (things they can't give to their clients) and uses them for things like shop rags and mop heads. So I would either donate to the organizations (who will not trash things that are recyclable) or I would look directly for textile recycling. We also have a local company that works with the Girl Scouts, and they collect styrofoam to use in unique ways, like in manufacturing picture frames. It's great because they use up the packing materials that come when you buy an appliance, excess packing peanuts, styrofoam coffee cups, and the trays from supermarket meat purchases.
I'd seek out appropriate organizations - in fact, if you can find a company that does textile recycling or an organization that is sponsoring a drive. You could expand it to let your neighbors know, or propose this for a community group that wants to do service or raise funds.