The main place I have donated quilts is to the regional CASA (Court Appointed Special Advocates) office in my area. They go to children in foster care. I've done that on my own and as part of a group at church. In the church group we've also made quilted door hangers for Christmas to give to the nursing home next door. I've also given quilted potholders to the local women's shelter.
Our group is also going to look into giving quilts to the county sherriff's office to give to the children they encounter on their calls.
I prefer to do my giving locally, where I know exactly who is getting the items and can drop them off in person, but that is just a personal preference. The ladies at the CASA office are always thrilled when I stop by.