I have received many American visitors during my time in Greece, and, as a result, I have visited the Acropolis seven times in two months. So when a friend stopped in for twenty four hours before his trip to Mykonos, he greeted me with a weird, but welcome, challenge: he did not want to see the Acropolis. My Greek pride kicked in and I was initially insulted, however, with a little brainstorming we developed an itinerary jam-packed with fun, tourist free activities. It went like this:
11 AM: Stop by a bakery, any bakery, and pick up patatopita. It’s the lesser known cousin of spanikopita, but it’s twice as addicting and terrible for you.
11:15 AM: Visit Phillipappou Hill, home of Socrates’ Prison Cell. Entrance is free and the brief walk up to the top is not strenuous, even after consuming a pastry made of fried bread and potatoes. From the top, enjoy a view of the Acropolis without all the tourists, plus a 365-degree view of Athens all the way to the sea.
12:30 PM: Walk down the street from Phillipappou Hill toward Monastiraki to get to Thissio, a neighborhood with a large pedestrian walkway, blooming purple flowers, and many cafes. Stop anywhere with reasonable frappe prices and request a backgammon board. Google “how to play backgammon” or ask a local. Order toast, which is really a cheap ham and cheese panini that generally looks like someone sat on it. 
2:30 PM: Take the metro to Panepistimio and walk through Exharia, a decidedly indie-rock neighborhood. The streets are lined with cafes and art galleries. Wander the streets, walking down toward Stadiou and crossing over to Koloktroni Square. Maybe, just maybe, coax yourself into the National Historical Museum. It only covers about 400 years of history, so you shouldn’t get too overwhelmed. If you need a coffee refill, head to “Booze” an old building renovated as a coffee shop, bar, and art gallery all in one.
5 PM-8 PM: These hours are lost due to a jet-lag inspired siesta.
8 PM: The perfect Greek dinner time begins soon! Take the metro to Monastiraki and walk the opposite direction to end up in Psirri. This nightlife district is filled with late night cafes, hookah bars, and bouzoukias (traditional Greek restaurants with live music). Opt for a bouzoukia and fill your plates with pastitsio, greek salad, and saganaki before settling in to listen to the singing and traditional instruments.
Midnight: Greek dancing begins. Be prepared to be pulled into a group circle! The steps, it turns out, are pretty easy to pick up when pressured by locals.
2 AM: Walk back to the hostel. Ask yourself if you missed out on Greek culture by skipping the famous ruins.