Mentor was a famous tutor/teacher
in ancient Greek mythology:

Mentor, Minnesota

Mentor, Ohio

Mercury was the Roman name for the Greek
god Hermes, winged messenger to the gods:

Mercury, Nevada 

Mount Olympus was the lofty home of the ancient gods.
From Olympus we get place names such as:

Olympic Valley, California

Olympia Heights, Florida

Olympia Fields, Illinois

Olympia, Kentucky

East Olympia, Virginia

Olympia, Washington

The nine Muses in Greek mythology were the ones who
inspired the arts, sciences, music and all things cultural:

Muse, Pennsylvania 

Neptune was the Roman name for Poseidon,
Greek god of the sea:

Neptune Beach, Florida

Neptune, New Jersey

Neptune City, New Jersey

Orestes was the tragic figure who killed his mother, Clytaemnestra, and was pursued by the Furies, in the tragedy Oresteia by Aeschylus:

Orestes, Indiana

Pandora (all-gifted) was the first mortal woman. Her curiosity made her open up a jar (box), which unleashed all the world's evils upon the earth:

Pandora, Ohio

Pandora, Texas

Paris was the Trojan prince who ran away with beautiful
Helen, an act which caused the famous Trojan War:

Paris, Tennessee

Paris, Texas