April, May, late September, October — The Sweet Spot
Comfortable temperatures (18-27C), manageable crowds at the Acropolis compared to peak summer, and pleasant conditions for walking, which is how you'll cover most of central Athens.
June to August — Hot and Crowded
Temperatures regularly exceed 33C, sometimes into the high 30s, with little shade at most archaeological sites. This is also peak tourist season, meaning long lines and higher hotel prices — visit the Acropolis at opening time if traveling now.
November to March — Quiet City Break
Cooler (10-15C), occasional rain, but noticeably fewer crowds at major sites and lower hotel prices. A legitimate option if your priority is history and museums over beach weather — Athens itself isn't a beach destination anyway.
Late September into October is arguably the best overall balance: warm enough for a Saronic Gulf island day trip, cool enough for comfortable walking around the Acropolis.