According to the Callimachus Hymn to Artemis, the goddess Artemis rarely goes to cities. She prefers to stay in the wild and spend her time hunting. The only reason she would visit cities was to help women in childbirth. So it is unlikely that Artemis would have a favorite city.
However, she is the patron of Sparta, and Ephesus and a huge temple in her honor.
Artemis the greek god of the hunt and of birth
The Greek goddess Artemis is the protector of:VirginsThe youngAnimalsWildlifeThe city of SpartaWomen in childbirthThe hunt
The Temple of Artemis was named after the Greek goddess Artemis, who was the patron goddess of the city of Ephesus where the temple was located. Artemis was the goddess of hunting, wilderness, and fertility, and the temple was dedicated to her worship.
The city-state for which Artemis was patron for was Sparta.
Artemis' city is often associated with Ephesus in ancient Greece. Ephesus was known for its Temple of Artemis, which was one of the Seven Wonders of the Ancient World. Artemis was a prominent goddess in Greek mythology, embodying aspects of the hunt, wilderness, and fertility.
Artemis is the patron goddess of the Hunt. She gives her aid to women in childbirth. She protects maidens and animals. She is the patron of the city Sparta.
Artemis was one of many goddesses and gods of the Greek people, and Sparta was one of the Greek city states.
In Greek mythology, Artemis was regarded as the goddess of the hunt, of wild animals, and of the wilderness generally. She also was thought to be the goddess of childbirth and virginity (rather an odd combination, but it goes back to her birth, where she gave her mother no pain).
Artemis, the Greek goddess of hunting and wilderness, was often associated with the wilderness and spent her time roaming and hunting in forests and mountains. She was also closely linked to the moon, and her sanctuary was located at the ancient city of Ephesus in present-day Turkey.
She wished to have no city to be "patron goddess" of. She simply wanted to rule the mountains
Poseidon had a favorite city, Athens. As you may have guested Athens is the Greek goddess' Athena, goddess of wisdom. Poseidon and Athena fought for Athens but, in the end Zeus gave it to Athena.
Artemis the goddess feels the need to protect:New born creaturesAnimalsMaidens or virginsWomen in childbirthThe city of Sparta