@Makedonas @Wumo Just realized the Acropolis Museum and National Archeological Museum are two different things. I went to the first, not the later.
I stayed at hotel near the "Plaka" district. I mostly explored the area around the Acropolis, Parliament, and Panathinaiko Stadium. I used one of the "all access" passes offered for the major archeological sites, which I made very good use of during my short time in the city.
I stepped inside the Church of Panagias Grigorousas, but I wished I visited a few more Orthodox churches. I wanted to go to the Athens 2004 Olympic Park, but I was too busy exploring other places. Plus, I wasn't big on spending money for transportation. The taxi ride from the Acropolis district to the Athens International Airport was NOT pleasant on my wallet.
I ate at a few places, but I liked the vibe of a place called "Cave of Acropolis," so I ate dinner there every night I was in Athens. They had live music and a nice view of the Parthenon.
If I were to return to Athens, I'd probably focus more on modern Greek culture, or areas outside the main tourist area. I normally want a very "authentic" experience when I travel to a foreign country (I want to know what daily life is like, and be engrossed on the local culture), but I felt like I needed to visit the big sites since I had the opportunity.
Outside of Athens, I'd be open to visiting Olympia/Patras, any of the islands, and maybe Thessaloniki as a tourist.