You will have booked the Gatwick - Athens flight that arrives at 20:25 (21:15 on Sat). With these late evening arrivals you need to spend a night in Athens before proceeding to the islands, one reason I no longer use easyJet.
There is no point staying near the airport if you plan to spend the first two nights in Athens, but for one night it would make sense. The earliest flight to Milos departs at 09:40 (2010 timetable), so you won't have to get up too early to make check-in an hour before departure, even from central Athens. The metro takes 45 minutes to the airport.
If you plan flying to Milos on Fri or Sun, there is no morning flight, and you would actually get there earlier by ferry. Also be aware that the flights to Milos are on small Dash 8-100 turboprops. These 30~ pax aircraft are more susceptible to weather cancellation than the jets that fly to larger airports.
What I would do is proceed to Milos the day after arrival in Athens, either by flight or ferry. No need to return to Milos from Sifnos — you can take a ferry direct to Piraeus. Then spend your last night in Athens, giving you all day for sightseeing before the 21:00 flight.