We stayed with Upstreet's Chic and Cosy Flat, which is located in a quiet corner of Plaka. They were very helpful in providing check-in instructions (lockbox) and asked us to let them know if anything was missing after we first got in. We took a taxi from the airport (€40) and the driver was able to locate the building perfectly. The location is excellent for visiting Plaka, Syntagma Square, and the Acropolis (a short walk through restaurants and stores to the main street). The apartment is spacious and comfortable, with air-con in both the bedroom and living room. The kitchen was accommodating for our needs and there's a grocery store a short walk nearby (Bazaar). We used their suggested service for taxi transportation to the airport and recommend it (https://www.welcomepickups.com, €61 for early-morning service). We would stay here again.
We highly recommend visiting the Acropolis in the early morning or late afternoon! We left at 10am and stood in line for a half-hour just to get tickets, then had to jostle our way through all the other visitors to get around. The Museum was also packed around that time, so we returned in the late afternoon when it was not crowded at all. You can also apparently buy your tickets ahead of time and just scan in.