Most people assume that if you visit one place in Athens, it has to be the Acropolis. I can't argue with the sentiment, but I can argue that the Agora is a much nicer place to visit, and it has some of the best spots to see the Acropolis. Once you get up the hill to the Acropolis, frankly it's a little dull. I think the temples look better from a distance, and most of the surface of the Acropolis is just covered in worn marble and piles of random rocks (which used to be parts of these structures).
The Agora has one of the most well preserved temples on its site, the temple of Hephaestus. All of the walls are in excellent condition, and some of the roof is even intact. Best of all it's surrounded by beautiful gardens and bushes. Right now they're working to fix up many of the buildings on the Acropolis, but at the Agora the Stoa has been completely restored. The building looks fantastic and houses several museums, including a recently opened second floor with a great view.
Historically the Agora is a very important place since it was (arguably) the home of democracy. The argument comes as many historians believe that this place was in fact not the first place to hold elections, but instead the first place to use ballots in an election. The secrets of the Agora have yet to be fully explored too, there is still digging going on, and regularly new finds are discovered.