Greetings Pedro!
Say hi to Norwalk for me, I lived there, worked there & loved it, for over a decade -- and made my first trip to Greece from there, in 1999. I hope you can put together a trip that both you AND your children will enjoy... b ut it does puzzle me that you are traveling halfway around the world for just 5 days??? You need to tell us much more, because you want good advice but do not provide enough information. I'm going to be blunt about your ideas, just because I want you to have a great time, and from what you have written so far, your wish-list is not informed & not realistic.
Your children won't like Santorini much because Greece it will be SO hot (up to 100°F) they'll want to swim... and Santorini beaches are black pebbles & grit ... feels like walking on a red-hot griddle! And you do NOT have to go to either Santorini OR Mykonos to see the white & blue buildings, these buildings are typical of almost TWENTY islands in the Cycladic group -- the fact that you think these are only on 2 islands shows that your research has not gone any further than looking at a calendar or a few swipes on your phone. PLUS these are the most crowded and Most expensive islands in the entire nation of Greece! If you only have FIVE days (and does that count the day you fly in, and the day you depart???), means you need to do homework, and be more realistic.
Frankly I don't think Knossos is in the cards for you, this trip, unless you ONLY do it, & Heraklion & stay nearby ... at a beach that probably will be MOBBED in August. I know one nice place in that vicinity that I can recommend that isn't totally jammed with British package-holiday throngs -- Mike's Place, in Annissaris nea Heraklion -- but you'll be limited in what else you can do around there -- and I just checked and its' totally sold-out for 1st 3 weeks of august. NOTE: the period between August 1 and August 21 is VERY likely to be totally sold out for family accommodations (i.e, 2-room units sleeping 4), all over the GReek isles, because August 15 is the GReeks BIGGEST holiday of the year next to easter, and those 3 weeks are the biggest for ALL European countries, since a huge percentage of the population gets all of August as paid holiday. Yes, I know ... but bad timing for North Americans.
If you have 5 days BESIDES the arrival/departure days, you can fly to ONE island ... and maybe, just maybe, after 3 nights you can ferry for no more than 1 - 1.5 hours to a 2nd Island. Then you need to FLY back to Athens the night before your departure day -- it is too risky to return from an island the same day as y our homebound flight.
Your priorities should be -- an island (or islands) that are affordable and enjoyable for a young family, where you an be close enough to a beach so that you can WALK there & not have to rent a car just to get wet ... for instance if you want to swim at Calf Pasture Beach you don't want to rent rooms by Stew Leonards, you want a place next to the Marina Mini-Golf Course. To see what's available/possible for you, I just did a "dummy booking" search on NAXOS and ANTIPAROS for 2 adults/2 children Naxos on PLAKA BEACH, and ANTIPAROS near a beach there.
NAXOS - PLAKA BEACH -- only about 15 places left for that 5 days, about $200 per night.. the nicest one is Filippa Studios, 2 br, about 50 feet from Plaka beach. Busses go every 30 mins from earl AM till late night, going to Naxos Town where there's lots to do & see ... FAB museum of Minoan artifacts, winding lanes, a castle, more more ... and you can rent a car for 1 day to drive all over the island, ruins & statues & history galoroe.
ANTIPAROS -- just 1 hour by ferry from NAXOS to PAROS then a 10-minute ferry to ANTIPAROS -- for the same dates, I saw Dimitris & Theodore Appartments 2br with sea view terrace, for $908 for 5 nights. a 5-10 minute walk downhill to a great sandy beach, shallow at the edge. From the isle's tiny Port, you can walk here, and that whole area of Antiparos is totally walkable. What is more you could STAY on ANTIPAROS, and take the 10-minute ferry to the port of PAROS and explore its fascinating Port Town. Multiple flights per day from PAROS airport to get you to ATH airport the night before your departure... and I can recommend a place to stay (with free 24/7 shuttle) near the airport that is ALSO on a beach.
However, dear Pedro, you come to us with a Big ASK -- You want to come for a VERY short stay, in THE busiest time of the year and you want to see a whole bunch of stuff, WITH 2 children. And unless you can give us exact days On the GRound PLUS time of arrival on Day 1, and time of take-off on Departure day, plus your budget limit for accommodation, how can people give you good advice?
Please share more, Immediately, if you want the best help.