Thank you, Susan Blair for recommendations in Crete. Here are some my picks in Athens. Please note it's likely that none of the restaurants listed below has English menu.
Ouzadiko: 25-29 Karneadou Street, Kolonaki. Everything's good here, I think. Melitzanosalata (everyone seems to be tired of this, but you ought to try well-made ones) is one of the best I've had. Rice dishes, maybe except dolmades are made w/ converted rice & are well-cooked (slightly mushy). Flavor is very good, but if you hate converted rice, avoid. House wine is very good. Although there's no dress code, dress smart-casual if you want to blend in.
Marabou: Panormou Street (near Panormou metro station). Simple, but well-prepared good quality food. Bread they serve used to be much better, but they still serve them warm. Seafood (grilled sardines, baby cod w/ skordalia are some of my favorites), hortopitta, country sausage, maidanosalata (parsley dip), kabourmas are good. If you want mussels, fried are better than saganaki. Wine (from barrel) here is very good, too.
Inomagirio: In Patralona (?). I don't remember exact location & is hard to find, but I like the food & atmosphere here. Zucchini & yogurt dip, fried bread, meatballs w/ leeks, slow-baked pork are favorites.
There are some better-than-average restaurants in Halandri area. A place called O tzitzikas ke o mermigas (?) had interesting dishes and, pork w/ caper sauce was quite good. Salad dressing was too sweet. Some of the other dishes are: chicken w/ almond & pomegranate sauce (sweet, but pomegranate seeds were nice touch), mussels in ouzo sauce (it was unavailable when I went).
The best taverna I tried in Athens was Kouklis, in the Plaka...absolutely wonderful everything, up just one little flight of winding stairs...I ate there more times than I'd care to admit during 3 weeks in Greece. And then there was the seaside cafe in Chania...baby squids snatched from the salty sea and fried crispy-crunchy, piled high on a plate with fresh Greek lemons to squeeze over them...aahhhhhh, and the sunshine on the Aegean...heaven.
very nice. a note on melizanosalata. it is grilled/roasted eggplant (aubergine) and olive oil and parsley, and salt and pepper and garlic and vinegar. it is, properly whipped with a fork by hand, but the restaurant varieties are, usually aweful and blended in a food processor and terrible and gloppy and not tastey.
As Gary says restaurant melitzanosalata are generally awful, but Ouzadiko's version is quite chunky & smoky. Another one I liked is Palia Istoria (Old Story) in Rhodes. I used to go there when I was staying in Rhodes and, I once had pork & celery stew w/ avgolemono which was quite good. I think they only do grilled meat in summer, but more interesting dishes in winter.
Useful website if you like Greek food &/or want to search Athens restaurants: www.gourmed.gr
It has restaurant reviews, but so far only Athens (& maybe some of the most popular islands?). I hope they'll do other cities & islands as well.