Go to the Acropolis, visit the place, but go in the afternoon, so you'll be around to see the sunset from that mount. Incredible visual. You may want to bring something to eat and drink and make a little picnic while looking the sun going down.
After that, you can go behind the Acropolis where you'll find small street (you can go there only by walking) where you'll discover small places to eat, low lights, old buildings. Magical.