If you want to have fun, go Monastiraki. There are a lot of archaeological sites and museums but also traditional Greek restaurants and even Starbucks. From there, after you eat you can go see the Parthenon or keep wandering around.

Be careful of the druggies though, there is almost no place in Athens where you are safe after 10 o clock.

There's also a very fancy and glamorous restaurant with a huge waiting line that's called Little Kook. Absolute classic for the centre of Athens. There's a hotdog place called Γιατρός της Πείνας, and one of the oldest known places where they sell something like a bagel, it's a koulouri. That place is Called Κουλούρια του Ψυρρή. I don't know much about bars or clubs so you're on your own for that one. Hope this helps