If you visit Athens you may choose to escape the city for a day and explore some of the surroundings areas. The popular choice in Greece for travel is the islands, and if you have 5 days or more it can be a lot of fun. If you really want to visit an island and you have limited time, Hydra is the closest, and best choice. An overnight on this island will gives you a taste of island life without huge travel time. However outside of Athens there are a lot of day trip options that can be really great to see.
If you want to stick to the mainland, there are many other options as well. Sounio is the home of the temple of Poseidon; this site is the perfect place to watch the sun set. If you're driving to Sounio you'll also pass some great beaches, perfect on a hot day.
If you don’t mind walking, Corinth is well worth a visit. With 4 key sites to see you can easily fill up your day. If you have the energy you should start with a climb up the Acro-Corinth, a beautiful fort on a hill. After the climb you can eat lunch in the village bellow and explore Ancient Corinth. Next head over to new Corinth and sit by the statue of Pegasus, after all he was born here. On your way out of town check out the world famous canal, an engineering marvel.
If you're in Athens for more than 5 days scheduling a day out is a great way to see some of Greece that you may have missed, as well as getting a little fresh air. Buses/boats are available to all of these destinations, inland you can also drive.