Hi there, we are spending only one day. Where should we go?
Acropolis/Parthenon and Plaka (Temples and market).
That's tough. I think if it were me and I had never been to Athens and had just one day, I would do:
- HOHO bus tour. I know a lot of people hate these, and I get why. I just like them as a good overview of a city in one day;
 - Plaka for lunch (or dinner if your daytrip is long enough);
 - I guess the Acropolis is a must do, but its a lot of up and down and queues for what I personally think is not a big enough bang. Given the short time I would rather just do the Acropolis Museum. Also its close to Plaka so minimizes travel time.
 
We had one day in Athens prior to our  going to our 1st Greek island.  We started with the Acropolis/Parthenon at 1 pm, spent an hour and a half there and then went to the Acropolis museum where we spent 2 1/2 hours.
Prior to going back to the US we spent another day in Athens seeing the other archaeological sites such as the Ancient Agora , Roman Agora and others. We walked through the Plaka which has many restaurants and souvenir shops. We didn't feel the need to go into any of the stores there as the quality of the merchandise is not great. If you are going to any of the Greek Islands on your trip you can find better quality souvenirs as we did in Milos and Naxos.
Do the New Acropolis Museum near the Acropolis and the Archaeological Museum.
HOHO bus is o.k. as transportation, but unlike many other cities, there is really nothing to see from the bus.
The National Archaeological Museum is worth a visit, especially the Mycenean gold