No answer yet from Original Poster, so who knows if she even came back to the forum ... also she notes trepidation at the idea of a 10-hour commitment.... so, hmmmm. Almost anything would involve at least an 8-hour commitment: You'd need a hour to get from Central Athens to either the ferry Port & Board a ferry... or take a Plaka area trolley to a fairlly nearby beach like Vouliagmeni. Cape Sounion -- a great ruin overlooking the sea -- excursions go there for the sunset, but then T EN busloads of people all elbow each other for snapshots! And public bus = 3 hrs each way. All the other options either $$ or time-consuming, or both.
Our inquirer tells us only"family of 6" Are there toddlers? Grandparents with mobility issues? Budget issues? Going anywhere except on Metro or city bus will require 2 taxis. Is this family in Athens after or prior to an island vacation? Or would this be their only chance to visit island? Unless we know the big picture we are just spinning our wheels.
TOmmy K has one of the least complicated/expensive suggestiona...island of AEGINA. If they can easily access the GREEN LINE Metro ( stations @Omnia & Monastiraki) they would not even have to change trains... a straight shoot, 20-30 mins, to PIRaeus, less than $2 each (OR 2 taxis, about €20 each). They can catch a "COnventional Ferry" (I.e. open decks) -- NOT a Hydrofoil (closed in/no view)... and enjoy a 1-hr "mini-cruise" ... watching the wake, seeng everything from giant cruise ships & freighters to 3-masted schooners, speedboats, and tiny sloops.. maybe even a dolphin. Aegina has a charming port town complete with a few ruins... a bus takes you to a mid-island ancient Temple atop a hill... a walk downhill gets you to a beach where u can have a dip & lunch at a taverna... back by bus or taxi to port & return to Athens @ sunset. Here's a photo album of a june daytrip: http://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/ Only challenge at all - to get to Pireaus in time for an 8:30 or 9 am conventional ferry.
As for Hydra -- it's much farther, and u can go only in closed-cabin hydrofoil.