I donate my art to charities all the time. When the charity of your choice holds an auction (many do, often once or twice a year) you offer them your art. Usually you can do this by emailing a photo, and they'll decide whether it's appropriate for their purposes.
Wisconsin Public Radio has auctions, for example. People can view all the donated merchandise on line and bid on line.
Anything you donate to Goodwill or St Vincents or whatever goes to charity too, obviously. But to allow the charity to realize as much money as possible from your donation I think the auctions are the way to go.