I think it really depends on what type or how much support the student needs. Many state schools in our area (New England) have decent support. We found a few schools that have specific LD programs with various levels of support for an additional fee. We also found small LAC's with supportive learning environments. We also found a college that accepts only kids with LD's.
It's also important to look at a college's graduation requirements. Foreign languages are often difficult for LDers. In our case, we needed a school that had a lighter math requirement than some, as that is D's primary area of disability.
Here is a short list of schools I know of that have fee-based LD programs:
Curry College (MA)
Dean College (MA)
Mitchell College (CT)
U of Arizona
Landmark College (VT) (LD students only, tuition includes services)
I know there are many others!
In our case, we felt that the LAC's without LD programs couldn't really offer the support she needs. D fell in love with Dean, but we couldn't afford it. She chose Landmark who, despite having the most expensive sticker price, gave the best financial aid package and was the lowest net price.