Athens is best in the shoulder seasons when the Parthenon isn't radiating August heat and you can actually walk the Plaka without sweating through your shirt. May and September give you long days, open air dining, and ancient stones without the brutal mid-summer sun baking the city.
A typical trip runs about $2800 for flights and a decent place to stay. Spreading that cost out makes it manageable, but you need a solid plan so you aren't paying for Athens long after you're back home.
That 0% intro window is a deadline, not free money, and any leftover balance when the 15 months ends will get hit with a high standard interest rate.