Kolonaki Platea (or Kolonaki Square) is the main "ritzy" square up by Lykavittos hill. Here is where you will find the Gucci and Prada stores as well as many nice cafes and tavernas. The Greeks who live here are mostly wealthy compared to the rest of the main part of Athens. They speak English and French (as well as Greek, of course), but a lot of the time they are pretty snooty when it comes to tourists. But the square is very nice to relax in and the shops are pretty amazing when it comes to things to buy!
One note about Kolonaki and Greece in general: The city and country is ancient, thus the plumbing is ancient as well. You will not be able to flush your toilet paper in many parts of Greece. Be prepared for this! But do not worry, Greece has very few Turkish Toilets (essentially a hole in the ground with plumbing) left; you will have toilets!