FIrst of all, AThens airport is NOT Athens ... it is 1 hour away by metro or taxi ... so you are not "STAying in Athens' by just landing at the airport. Second, if you have read any of the Greece forums at all -- this one or Trip Advisor or FOdors -- you'll know alreadly that all of us "GReece vets" strongly recommend Athens LAST. Main reasons:
• Timesaving - on your very short trip, you waste precious hours checking in/out of Central AThens hotel
• Recovery from jet-lag easier/more fun on an island
• Island time allows u to figure out "how Greece works," makes u efficient at navigating bustling world capital
• Even a few days exposure to Greek history/culture on isle makes Athens world-famous landmarks & museum treasures more meaningful for both kids/adults -- so no, don't "SKip" Athens -- if that's the outlook, why not just go to Carribean ...
Workable option:
• Avoid long-distance ferries (u lack timei); only ferry - between the 2 isles (except necessity-option below)
• FIRST PRIORITY - check availability of FLight for 6 TO Santorini on Arr, and from Naxos BACK To ATH in time to allow 2 full days there - if no flight available back, then must take Blue Star Ferry 6pm -11:45 (get 'reserved economy' seating) to Piraeus
• On arrival, allow 2 hrs layover, take 1st available Flight to Santorini (BTW, giving exact date/time arrival produces best advice) I hope u arrive am of FRI or SAT: Fri Noon - Monday AM is when fewest Giant Mega-Cruisers Dock & hordes invade
• SANTORINI - allow 36-48 hours Max (2 nites) - it's all about "famous Caldera View" -- beaches are n.g. -- Try to book lodgings on/near Cliffside view in FIROSTEPHANI ... because no need rent car, you can walk to/from FIra town but stay outside hubbub
• DAY 3 - Ferry to NAXOS 3:15pm (BLUe Star arr 5:30) -- Look for beachside lodgings on Plaka Beach; local bus connects w port town hourly, takes 35 mins runs til midnight; to explore island u either need to rent 2cars or 7 psgr van IN advance OR (good option) local KTEL bus tour 9-5 with swim stop (€23 each) -- lots to discover all over island & in fascinating port town. The ideal family/active discovery island... we can't tell all here, u need to research.
• DAY 9? 10?- either Fly back to ATH in afternoon or BLUE Star in evening - 2 taxis to lodgings in Central Athens
• FINAL 3 nights/2 full Days --ATHENS - https://www.orangesmile.com/destinations/img/athens-map-big.jpg is swell online map (CLick & it gets huuuuge) PLEASE book place walkable to Acropolis & all major landmarks ( Plaka, Makrigiainni, Aerides, Monastiraki, Koukaki, Kolonakii) -- TIP: booking dot com now has large pvt apts to fit all 6 of you, short-stay, at better rates than hotels -- do NOT get lured by fancy fotos into VRBOs waaay far away.
NOTE: Starting late, w large group, for popular destinations at popular dates (HIGH SEason begins july 1) -- you will pay top dollar -- but the above itinerary option has proved the most workable & fun, for all the family "newbies" I've advised for 20 years.