Defining suburb can be pretty tricky especially in places that grow out rather than up. In the Atlanta metro, Fulton county must be urban because it had Atlanta in it, but is N. Fulton really different from Cherokee or Forsyth? DeKalb is suburban because it was the first suburban county in Georgia, but is it really much different than Atlanta now?
I think the perimeter is a fairly good boundary. As for Hawaii, I'd consider anything north/west of Pearl City/Aiea plus Kailua/Kaneohe to be the suburbs.