Is this something that is an inherited piece or a purchased item !! If its an inherited piece that has some link to your family/area/county ect. Then you might consider the local historical society !! Especially if the family has lived in the area for a long time !!
You could also consider a charitable donation !! Of course it would likely be auctioned off in order to raise money for the charity !! Hopefully someone that has an interest in antique clothing would be the buyer !! That would also give you a tax deduction !!