Eureka, California
"Eureka" received its name from a Greek word meaning "I have found it!" This exuberant statement of successful (or hopeful) gold rush miners is also the official motto of the State of California. Eureka is the only U.S. location to use the same seal as the state for its seal.
Eucla, Western Australia
The name Eucla is believed to originate from an Aboriginal word "Yinculyer" which one (uncited) source gives as referring to the rising of the planet Venus. It was first used by Europeans for the area at some point before 1867.