Use this map below and play with your dates, a lot of options to get the 4 flights for under $350 and see an interesting destination. Or you can book these separately and see ATH or SKG, too. The sooner the better though because you are too close to the dates and fares are going up....

https://www.google.com/travel/explor...vnKkA&hl=en-US

Now mind you visiting Greece in July, and for the first time, as a side trip just to get the 4 flights is offensive, but what are you gonna do, lol...