Athens is not a city that rewards the stopover format. It has been treated as one for forty years and this has flattened most people’s understanding of what it actually offers.
The Acropolis and the Parthenon are where you start. Go at opening, before the tour groups arrive. The Acropolis Museum below is one of the best archaeological museums in Europe and is routinely skipped by visitors who have a flight to catch. Do not skip it. Budget three hours.
The archaeology in Athens extends well beyond the Acropolis. The Odeon of Herodes Atticus, still used for performances and visible from the south slope of the hill, is one of the most intact Roman theatres anywhere. Sounion is an hour from the city and worth the drive: a Temple of Poseidon on a cliff above the Aegean, at sunset, with very few people.
Syntagma is useful orientation but not the Athens worth finding. Walk south into Koukaki, or north into Exarcheia. Eat somewhere without a laminated tourist menu in four languages. The city has a serious food culture that its reputation as a transit point has historically obscured.
One day in Athens is possible but it is the wrong question. Three days is the minimum for the city to make sense. The hotels with Acropolis views are worth the premium, once, for the specific experience of seeing the Parthenon lit at night from your room. After that first night, move to a neighbourhood.