You'll need more than a day...Have you been there before? If not, here's a short list:
1. Acropolis; it will take a lot of time but it is worth every second. It's good time of the year, I visited it in July twice and it was very hot. Anyway, be prepared for some nice walk and visit the museum there. It is just amazing.
2. The Grave of Unknown soldier; it is in the center and you'll see guards in traditional dresses. Very interesting
3. I hope you'll have a night there too. In that case, visit Plaka and have fun!
4. I would suggest you Glyfada for some plane spotting, but good old Helliniko is closed
, so, you might rent a car or take some bus and go all the way down to Sounion and see sunset. It takes 40-45 minutes from Glyfada and you'll see some wonderful scenery.
5. Eat some gyros for me, please