Should I rent a car?
A car is not only unnecessary in Athens, it will be a nuisance as you will have to find parking (it’s scarce!) and make your way in congested streets lacking clear signs and directions. Instead, the most convenient and easy way to get around is by taking the very efficient metro, the bus, or walk around. Distances in the city center are not great, and you can walk to most touristy attractions in less than 30 minutes. In case you do want to get around quickly, you can find a taxi without any trouble, and it is also inexpensive. See here Tips about taxis.
(If you do rent a car, don’t forget to get parking cards from the kiosks and put them in the front window of the car to avoid getting heavy fines or even get your car towed away.)
HOWEVER, if you wish to take day trips around Athens? You can of course use intercity buses but renting your own car will allow you to get to more places at your own pace, and in the comfort of your own vehicule.
Important Note: Legally, in order to rent and drive a car in Greece, you need to have an international driving license. Some rental companies will not insist on it, but others will.