Bumping this thread in case it's helpful for others too, who will benefit from this information.

In case anyone is traveling with someone in a wheelchair and you aren't getting a rental car, here's a list of the airport Hyatts with an airport shuttle and if they have an ADA-equipped vehicle or not:
Hyatt Regency Dulles: No, no alternatives
Hyatt Place Herndon/Dulles-Airport East: Yes, but 24-48 hrs notice is recommended
Hyatt House Sterling/Dulles Airport North: No, no alternatives
Hyatt Place Chantilly/Dulles Airport South: No, but will pay for Washington Flyer (accessible) upon arrival
Hyatt Place Sterling/Dulles Airport North: No, but will pay for Washington Flyer (accessible) upon arrival

DCA:
Hyatt Regency Crystal City: Yes, but 24 hrs notice is recommended

*Info current as of 8/14/23