Just like NYC, location is key. Where in DC you want to live depends a lot on commute and budget. That being said, I think Montgomery County offers the most ASD resources.
For pre-K, there are autism preschool classes. In K, there are Austim classrooms or Learning Centers. Starting in 1st, there is an Aspergers program. There is also a Social/Emotional program. There is some overlap between the services of the programs and you would get a chance to talk with the program coordinators and tour the schools. All of these programs are open to students that live in the county and it doesn't matter where they live--meaning you don't have to live within the school boundaries to access these programs. But placement does come through the IEP.
https://drive.google.com/file/d/1xnN_1KhKgrnNU5dKLSP3EQOOJWUlXF1k/view
On a private level, in Mont Cty, there is Ivy Mount and Katherine Thomas. There are other private options as well--it all just depends on the specific profile of your kid.