Hi there! I lived 2 years in Greece and Eric's explanation is pretty good!

If you stay there 10 days, you definitely have to focus on Peloponese (Nafplio is beautiful), Olympia, etc... rent a car in Athens (avis, hertz), it's pretty cheap.
If you do not like too big cities, don't stay too long in Athens... Athens is a great town, especially now with the new metro (built for the Olympic games). Travel with metro and cab but NEVER with a rental car or with motorbike.
Athens is crowded, very busy, impossible to walk on sidewalks, very very noizy and polluted! a lot!!! so there, visit the typical things like the Acropolis, the National Museum, Lycabetus hill, and if you have some time, go to Cap Sunio! It definitely worth it! 1hour from Athens with bus. It's the temple of Posseidon and it's just magic there! temple on the sea! just great!
In Athens, avoid tavernas (typical greek restaurant) in Plaka... they just cheat on tourists!
Greeks are very friendly but if they see you are a tourist and it's your first time in greece, they will try to cheat on your for everything... be aware with taxi drivers as well... have a look on the meter!
When you hire a cab, shout from the street... the driver won't stop to know where you want to go... sometime you will make the drive with 2 other people you don't know and who go to the same part of the city!!! be aware that you won't be able to share the drive with the others! you will have to pay your own drive, the other passengers as well!
This is greece

Chaos but great
If you have some time, after Athens and Peloponese, go to the islands (Cyclades are the closest ones). Santorini is pretty far (1 night by boat), but the journey by boat is simply great, especially the arrival there, in the volacano! Something you don't see by plane.
Paros and Naxos are great islands, and there, easy to rent a motorbike!
I would say that in 10 days, if you really want to see something and to enjoy greece, greek food, culture, etc... the visit of Athens and Peloponese is enough! Islands take another 2 week vacation
Enjoy there!!! you will love it
JASSAS!