Try www.whichbudget.com to see which low fare airlines fly which routes. You might find europebyair.com helpful for you specific itinerary, too.

I haven’t much experience with Greek Islands, but..

Mykonos and Santorini are good choices if you have limited time to island hop as they are easy to get to from Athens. They are both picture post card scenic. Both are the classic white buildings and rocky shores. Mykonos has the iconic windmills, Santorini has the iconic blue roofs. Because of their pluses both tend to be a bit touristy and expensive.

I like Rhodes — big enough to have lots of variety — ancient ruins and history, crusader medieval ruins and history, beaches, nightlife. It is farther from Athens so somewhat more difficult to get to. Consider renting a car if you want to get to uncrowded beaches.

Vueling flies that route. The cost on the early morning flight is less than half that on the later flights.