Hmmm... There are lots of places... You already been to the mountains and I guess that you are not gonna go to the mountains in Greece... You'll probably go to the beaches huh?
First of all, if you -have- to go to Athens try not to get mugged around Acropolis... Acropolis, as much as I dislike Athens is actually pretty impressive. Second. There are lots of water related accidents every year in Greece too... People come over, get stuffed with ouzo and calamari under the sun all day and then go night swimming... well you get it I hope... Get sunscreen, lots of it.
Also, the small parts of Greece that fill with tourists in the summer, quite often don't have too many doctors, or ambulances so try to keep safe too.
But don't worry. Tourism is Greece's basic product and the quality is actually quite good. Every time I go holidays in Greece I feel like I'm suddenly in a new country...
Lots of the islands don't have any trees either... There are a couple who are a bit greener and cooler...
I would suggest having a look in this book:
Plus keep in mind that it might be cheaper to come over with an organized tour with other people from there instead of organizing the whole thing alone... But also check if you can get away from the group to check some stuff you want too.
Not the tourist hangouts huh... Hating mainstream is too mainstream!
There are some tiny islands which don't have -anything- on them... Some people go there...
I just go to the middle peninsula of Halkidiki... A friend of my mom has a hotel there and I feel kinda comfy there too... It has supermarkets to buy beer, small restaurants with good food and small family hotels near the sea. I wake up, have big fat doobie... Go swimming, return to the hotel and eat and drink beer... Holidays are not supposed to be exhausting you know..
I don't mind the countless eastern European tourist girls either!
Check the book... Can't really tell you a place to go unless you get a tiny bit more specific... But I would suggest to avoid Malia in Crete, Faliraki in Rhodes, Athens altogether and all the huge hotels... and Carrol Beer...