I studied in Athens for a semester in college and was so happy to get to go back with my husband!
Many people say that Athens is not really worth it, that it's not a great city, but I disagree. The juxtaposition of ancient and modern is so interesting. The Acropolis is wonderful, and at night it is especially beautiful.
You can easily fill up a week with all there is to do, however even one day is enough to see the main highlights:
Acropolis, Acropolis Museum, Ancient Agora, Roman Agora, Mars Hill, Monastiraki, Plaka, etc.
Going to the Acropolis when it first opens in the morning is breathtaking. It is nice and quiet with few people around, and you can get some good photos.
Also, public transportation is so easy and convenient. The Metro is clean, simple and easy to navigate.
The atmosphere is relaxed, even though it's a busy city. No one is in a rush, and the ambiance is so inviting.