It is one of the ironies of history that we know so much about the Spartan city-state, since the Spartans wrote nothing. All our written sources about Sparta were written by outsiders, primarily Athenians. So anything written about Sparta is by its nature an “outsiders” view.
How any other Greek city-state’s citizens thought and felt about Sparta was directly related to how often they were attacked by the Spartan army. For example Argos and Thebes were subjected to multiple invasions over the course of time and came over time to hate and resent the Spartans. Whereas cities allied to Sparta in the Peloponnesian League, such as Corinth and Elis looked much more favorably on Sparta, since they received security and protection from outside attack by being allied to the militaristic Sparta.
It is therefore odd that the ancient writer Xenophon of Athens clearly admired Sparta, even though he had fought against the Spartans in the last stages of the Peloponnesian War. He resided in Sparta after that war. His sons were sent through the Agoge; the rigorous Spartan school system that trained the awesome Spartan warrior.
It was the large, well trained and fearsome Spartan Army that caused many of the other cities to fear and hate Sparta. However, it was also this military machine that many cities admired. After all, only Sparta had the armed might that could enforce the every four years ceasefire for the Olympic Games. Further, when all of Greece was threatened by the Persian Empire, it was to Sparta that the other free cities turned to lead the combined resistance to that invasion.
Much of the loathing of Sparta also came from its system of helotage. In that system, Messenian helots were essentially agricultural serfs, tied to the land and supporting Spartan warriors. The Theban general, Epaminondas hated the helotage system and was the first general to invade the Spartan homeland and free the Messenians.
Another irony of the Spartan system is that some other Greeks such as Aristotle thought the Spartan were soft because of the way they treated their women. In other Greek cities, women were very much second class people. They could not own or inherit land, they were not taught to read, write or do any math. Generally they were completely separated from men other than their husbands, fathers and sons. In Sparta, women while not equals to men were certainly better off than their sisters in the rest of the Greek World. In Sparta, women were educated much like the Spartan men. Women learned to read, write and do sums, so they could manage the home while the men were off fighting. Further Spartan women were given physical education. They would often compete in the nude with the boys in foot races and wrestling. They also wore their tunics so they could move freely; this earned them the name disparaging “thigh-flashers.”
It is fair to conclude that the feelings of ancient Greeks about Sparta are mixed to say the least.