GreatSchools community has members from across the U.S., but it's hard to know about every school in every location...My son has LDs, although not Down's, and I'd suggest that the best way to get information for any child with special needs is to contact local parent support groups for the condition your child has, in the area you live in (or want to move to.) Other parents are often your best, most reliable source of current information. They can probably also give you names of good doctors, etc. I did a quick "google" search and came up with this Arkansas organization: www.ardownsyndrome.org/
There are probably others, but it's a place to start. Best Wishes.