What should one do in a 2 days trip to Athens ?
Acropolis of course, although our most memorable moments in Athens were watching the sunset, once on the top of Lycabettus Hill (you can either make reservations at the restaurant, amazing atmosphere, terrible food--or just crowd in with others at the lookout) and once exploring the winding walkways of Anafiotika. We were virtually alone here--it was fabulous.
Take a look at the below activities in Athens
Athens One Day Tour (you will get to see all in a day)
Athens Bike Tour (if you like being active ;) )
Athens by Night Tour (for a more romantic approach of the city)
Athens Dance with the Greeks Tour (this one is fun!)
Athens Food Tour (to have a taste of the local food)
Athens Sightseeing & Acropolis Museum Half-Day Tour (to see the must sees)
Temple of Poseidon and Cape Sounion Tour from Athens (to go a bit out of Athens)
Otherwise take a look at all things to do in Athens
PS: i am working for Tourboks and i am Greek so i could help you further if needed :)