Most of the Sumerian gods were to have lived on earth. Each had his or her own home in the temple inside their respective city. Lesser gods served the greater gods as workers, building the cities and temples, before humans were created. Humans were created to do the works of the lessers who complained - because of the first strike action, over working conditions.
Below are a few Sumerian deities in their respective cities:
An lived in Uruk (or Erech)
Enlil in Nippur
Enki in Eridu
Nanna also in Nippur
Inanna also in Uruk (Erech) and Kish (An and Inanna shared the same temple in Uruk)