Under which field of computer science does cloud computing fit?
According to the ACM classification, cloud computing belongs to:


Distributed architectures, under Architectures, under Computer systems organization.
Network services, under Networks.
Distributed systems organizing principles, under Software system structures, under Software organization and properties, under Software and its engineering.
Storage architectures, under Information storage systems, under information systems (as Cloud based storage).


So cloud computing is at the intersection of Computer architecture, Networking, Software engineering, and Information systems.

Cloud computing could also be considered its own area, since it has a dedicated conference, SoCC.