Paros, Rhodes, Crete, Zakinthos, Kerkira, Chalkidiki, Skiathos, Ios, Kos
All these places are cheaper than Myconos and Santorini but with amazing nightlife and ages in the range you provided.
If you are interested for the mainland, you would better visit a city with significant population of students, like Larisa, Ioannina, Rethimno, Komotini, etc but summer is not the ideal time to go there, better in autumn
You can also ask for advise from 2 top members of our forum
@vladimirosA and
@Kalogero who are expertise in tourist guiding, they can show you the best places and offer you some of your best nights of your life