In college, I spent a semester in Greece, and had the time of my life. I was part of a group of students studying there together and together we explored Athens, the countryside, and the islands. Each part of Greece - city, mountains, islands - is unique and amazing in its own way. I have so much to say about this wonderful country, but here's a overview:
Athens is a very nice city. Fairly clean, lots of trees and parks throughout, easy to navigate and clean metro system, and very close to the beach. A wonderful mash of ancient history and a modern, vibrant city. I got to live like a local for a short time and explore the neighborhood we lived in, eating delicious food, doing lots of shopping, and drinking lots of Frappe! The Plaka is super charming. Influences of the Byzantine rule remain, and you feel like you're in another world as you snake through the small streets, every now and then turning a corner to look up and see the Parthenon. Rooftop restaurants abound and what a treat that is, to have the lit up Parthenon as your backdrop while eating dinner til late in the night.
Glyfada is a nearby beach area. If you are in Athens and are not able to get to an island, Glyfada is great. There are some nice clean beaches, some private some public. It's just a train/tram ride away. (You can get all the way from the airport to the beach by the metro, FYI). Piraeus is the port, from which it is easy to grab a ferry ticket at any of the little ticket windows/shops and hop on a boat to whisk you away to an island. Some islands are just a couple hours away and can be done in a day trip. My friends and I went to Santorini, Mykonos and Poros.
Santorini is simply special. The picturesque town of Oia (pronounced ee-a) is the one you've seen on postcards, the little white churches with blue domed roofs. The caldera is a sight to behold, as well as all the little buildings spilling over the cliffs. Santorini is home to a black sand, white sand and red sand beach. However this is not the best island for laying on beaches all day. This is an island to explore during the day and enjoy the sunset at night.
Mykonos is the "party island". We went in early April so it was still quiet and almost no one was there, so we just enjoyed the beach. The main town (Chora, which simply means "town" and the name of many towns on many islands) is very very cute and charming with winding little streets lined with shops.
Poros (not to be confused with Paros) is in the Saronic Gulf, just a few hours from Athens. A quiet and beautiful island, this was a perfect weekend getaway from city life.
I'm going back to Greece next year with my husband. It'll be 11 years since last time I was there. And I cannot wait!