Various islands are possible via internal flights, and none are more than an hour's flying time. This works if your flight in makes a good connection. If not you are faced with traveling back and forth from the airport which adds to the time wasted.
One possibility you might consider is two or three nights in Andros. It's a beautiful island and has the advantage of being reached from the port of Rafina, which is much closer to the airport than Piraeus the main port. It is also much smaller and therefore easier to manage.
We go to Andros a lot and have written up our thoughts here
In terms of travel you can get a bus from the airport to Rafina (40 minutes), a ferry (2 hours) and then a bus (1 hr) across the island. Coming back there is a direct bus from Rafina into central Athens (1 hr).
Again, the issue might be flight times. Except at the weekend the ferries tend to go early morning, which might leave you overnighting in Rafina. A nice little town with some good eating places, but might not be what you want to do.