Most often Athens, which was named for her.
Athena was to look over Athens
athena's hair was curly
she was named after a town
If by Greece's most important town you meant Athens. It was Poseidon that Athena quarreled with over it's naming.
She gave the, at the time unnamed, town of Athens the olive branch. Her and Poseidon were having a bit of bet on which person could give a better gift. Athena gave the town the olive branch, which could be used for medicine, food, and crafting. Poseidon however struck the ground with his trident and gave the town a well. However, the water was salty and unfit for drinking. The people preferred Athena's gift and so they named their town Athens in honor of Athena.
The story of Athena's olive tree is: Poseidon and Athena once we're fighting over a town so they decided to see who could give the people of that town the better gift, Poseidon gave them salt water that helped for nothing at all, and Athena gave them an olive tree.
Athena and Poseidon both wanted to rule this one town so to settle it they both had to give gifts to the town and the best gift wins the control of the town. Poseidon went first and he gave them a spring at first it was great but then the people tasted it and it tasted like saltwater from the ocean. Athena went next and gave the people an olive tree and it gave the people food, oil, and wood. So they picked Athena to rule and now the town is called Athens.
No, the temple and city/towns were named after the Greek goddess Athena. They were named after her in remembrance to her, for favor/patronage, or for worship.
Athena was the goddess Arachne challenged to a weaving competition, even though she was a mere mortal. She bragged to everyone in her town that she was a better weaving than even Athena. Later, Athena turned Arachne into a spider. So, the main characters are Athena and Arachne.
In classical mythology, Athena didn't have any children. She was a virgin goddess.
Gives him advice where to look.
She did not, one story in Greek myths tells that Athena and Poseidon fought over a town to see who could give it a better gift, Poseidon gave them salt water that did nothing for them, and Athena gave them an olive tree.