Map from Google - Athens

In Athens, capital of Greece, the climate is Mediterranean, with mild and moderately rainy winters, and hot, sunny summers. The city is located near the 38th parallel, but in winter, from December to mid-March, it's sometimes subject to outbreaks of cold air from the Balkan Peninsula, which can bring cold and rain for some days, and sometimes even snow. Snowfalls occur more easily in the north of the city; at the center, the Acropolis is whitened by snow more easily than then lower surrounding areas; a particularly abundant snowfall, which affected also the southern and coastal areas, occurred in February 2008.
Summer is hot and sunny; in summer Athens is the hottest capital of Europe; in July and August the temperature reaches quite easily 95/97 °F, but sometimes even 105 °F.
Precipitation is not abundant, since it amounts to about 15.5 inches per year, and follows a Mediterranean pattern, with a maximum from November to February, and a minimum in summer, when clear skies prevail and there are occasional thunderstorms.
Here is the average precipitation in the Ellinikon Airport.
Average precipitation - Ellinikon
Prec. (in)21.61.610.

The city covers a wide area in the plain of Attica, and is surrounded by mountains on three sides, and open to the sea to the south. Thus, there are slight differences that are worth considering, looking at data of four stations, from north to south.

Athens, position of the weather stations

Let's start from the Tatoi Airport, located in Decelea, at 800 feet above sea level, on the northern outskirts of the city, close to the foothills of the Parnitha mountain range. Here the average temperature of January is 45.5 °F, that of July is 78 °F; precipitation amounts to 17.7 inches per year, with a maximum of 3.3 inches in December and a minimum of 0.2 inches in August. Here are the average temperatures.
Average temperatures - Tatoi Airport
Tatoi AirportJanFebMarAprMayJunJulAugSepOctNovDec
Min (°F)373941465461666661544641
Max (°F)545559667786909082736355

Further south, near the park of Nea Filadelfia, in the north-central part of the city, 3.7 miles from the center and 440 feet above sea level, the average temperature ranges from 48 °F in January, to 81 °F in July. Here rainfall is just scarcer, 16.3 inches per year, being a bit lower in winter.
Average temperatures - Nea Filadelfia
Nea FiladelfiaJanFebMarAprMayJunJulAugSepOctNovDec
Min (°F)414145505764707063555045
Max (°F)555761687988939184736457

In the National Observatory, at the city center and not far away from the Acropolis, 330 feet above sea level, the temperature is higher, almost 50 °F in January and 82.5 °F in July, and is affected by the urban heat island. Here the rainfall amounts to 15 inches per year, so it's even lower, and it does not go above the 2.6 inches of December.
Average temperatures - Athens
Min (°F)454546546168737366595246
Max (°F)555761707988919184756457

Going further south, we arrive in the old Ellinikon Airport, located on the coast, in the extreme southern edge of the city. The temperature ranges from 50.5 °F in January, to 81.1 °F in July and August. Rainfall is very similar to that of the center, and as we have seen it amounts to 14.5 inches per year.
Average temperatures - Ellinikon
Min (°F)454546526168737368615448
Max (°F)575761667584909082736659

The amount of sunshine in Athens is great in summer, when clear skies prevail, while it's not so high from November to February, when the sky is often cloudy, although there may be sunny days also in midwinter.
The sea in Athens is warm enough for swimming from July to September, when the temperature is 75 °F; in June it's still a bit cool, about 70 °F.
Here are the average sea temperatures.
Sea temperature - Athens
Sea (°F)615959616470757575706663

When to go

The best times to visit Athens are spring and autumn, especially from mid-April to late May, and from mid-September to early October; from mid-October the likelihood of rainfall increases, which sometimes can be violent and concentrated in time. Those who don't suffer from the heat, can also choose the summer.