You'd never know it from the PR machine that is the Acropolis, but there are other ancient ruins in Greece. Entrance to one such ruin is included in your ticket to the Acropolis, and it is the Temple of Zeus. (hint: if the wait for tix to the Acropolis is long, go to Zeus's temple first, and get your ticket here.)
While clearly not the primary tourist attraction, the site of Zeus's temple is large, fascinating, and offers a different view of the main attraction, the Acropolis - you can see the wall built around the Acropolis that makes it a strategic military point. (You can also see Zeus's temple from atop the Acroplis, fyi.)
What I found so jaw-dropping is that this particular site is reached by crossing a main road (pollution, anyone?), power and phone lines are hung everywhere, and it's really like a park in the middle of houses and businesses.
To reach Zeus's Temple, you pass under Hadrian's Arch (along with the phone lines), which was the entrance gate into the city, built by those power-mongering Romans.
Originally, there were over 100 columns that supported the Temple of Zeus. Now, there are only 15, and one column that was blown over in the 1800s and left on the site, which I think is kinda cool. It really gives insight as to how columns are built, and the column pieces look like neatly organized crackers on a snack tray.
If you have one day in Athens, just get a glimpse of this site from the Acropolis. If you have some time, however, this is a good photo-op stopover. And, an easy walk from the Acropli Metro Station. (Quick note about the Greek subway - it's super convenient. The more touristy areas have new stations and trains - thanks to the 2006 Olympics. But even the older trains (non air-conditioned) get you where you need to go.)