THinking about the kids' interests, AND travel time, and having planned trips for many families like yours, I would totally go with the recommend about Skipping Delphi & concentrating on Aathens/ Nafplio area... especially since yours is such a short trip. The Many Reasons include:
• DELPHI is a looong drive (3.5 miles each way) and really is most appreciated by adults with deep knowledge of classical Greece, not "Percy Kiddies". By contrast, NAFPLIO is an easy pleasant drive on modern divided highway -- only 2 1/2 hrs nonstop (tho I do have some suggested stops). Nafplio itself is a wonderland for kids -- A Huge Fortresss atop a "mountain" plus Castle walls & parapets looming over Old town & a Fort in the water! And it's at the tip of a peninsula, so it can feel like an island. PLUS, important with Oct. weather uncertainties., plenty to do if there's rain. Here is the superb Noncommercial website that tells ALL -- exactly how to get there -- what to see - do - eat - where to stay - http://www.visitnafplio.com/ and a photo album of highlight of Old TOwn & surrounding famous ancient sites - http://www.flickr.com/photos/stanbr54/sets/72157632094108982/\ Study it Before you go!!
Here are my tested suggestions:
• ATHENS - Day 2: Percy Jackson AM TOur sounds good. Acropolis Museum has nice glassed-in terrace cafe for lunch; you can use it even if not doing museum. IF you decide on Museum, ask at desk for audio guides, which they claim now to offer. NOTE: for the klids sake you might go to TOP floor first, because it has Very good 20-min video (cartoon & live action) that dramatically shows turbulent history of Parthenon. Then work your way down Day 3: ?? The Syntagma Guards Exchange (hourly on the Hour) ?? Kotsana Museum of Ancient Greek Technology - fascinating mechanisms! Also National Gardens by Parliament? NOTE: while still in ATH, study this superb noncommercial website - http://www.visitnafplio.com/
• NAFPLIO & AREA - DAY 1 -- Leave - Taxi/car service (€40 flat rate) to ATH Airport pick up car - this google map - https://tinyurl.com/ysbmwn4d - shows route & possible stop driving to/from. Road bypasses athens, no stops Till AFTER corinth Canal 15 miles -- I rec. 1-hour stop at ANCIENT NEMEA.... the "runner-up Games Site" to Olympia" ruined colums, and terrific authentically restored Stadium where kids can run from racing-blocks 2400 years old! (Visit Nafplio gives Details!) - from there a 30 min drive to Nafplio....in time to browse Old town before sunset. DAY 2 -- Fab small museum in Main Square has the world's ONly exisiting Odyssey-era Warrior Armor!! Afterwards, find elevator IIN cliffside (see visit-N) up to tower & parapet... great views. Before sundown, loical playground at edge of Old Town is great kid fun. Day 3 -- Palamidi "mountain FOrtress" -- tip: you cn drive UP back way, one parent, plus kids, can walk DOWN the 999 steps; other parent drives car back & awaits them in cafe at foot of stairs. do you want an Iliad FORT without crowds? TIRYNS is right on road, just outside Nafplio -- HUGE boulders the size of Volkswagens, great climb to lofty views, NO tour busses. DAY 4 - early start -- drive across "THumb" of Peloponnse (see map) to Anacient EPidaurus!! Forget the acres of rocks, just go to Stunning Theatre - World's most Perfect Acoustic Arena, 15,000 seats. Send kids to top row so they can hear whispers from onstage. Drive onward to shore & Up toward ISTHMUS, the town of Corinith Canal. Take a few mins to walk out on Old Bridge (scary) & look down (so deep!) & take pix. Then connect to biggie highway back to airport. IF this is your last night before homebound flight -- consider staying at HOTEL AVRA. It has free shuttle (IF you book it at same time as reserving rooms) just 20 mins away, in Rafina. nice town square nearby for final dinner, then shuttle back to airport for flight.