It helps us give better advice if you state length of trip: 12 days? 14? NOT counting travel to/from Here are my thoughts. First of all, we "Vets" (me = 13 trips) always suggest ATHENS last? You'll be much more refreshed to tackle busy Athens -- AND more savvy about sight-seeing, Plus world-famouslandmarks will mean much more. Of course u may arrive exhausted & jetlagged not ready to drive. There's a great Answer, HOTEL AVRA, 25 mins away, overlooking a beach. FREE shuttle from/back to airport if you book at same time as rooms. Get thyself to Avra, swim, early dinner in tree-shaded town square, sleep. Next AM, shuttle to Airport, get rental Car, start your pelops Adventure!
This Fab Map -- https://euro-map.com/karty-grecii/peloponnes/podrobnaya-turisticheskaya-karta-peloponnesa.jpg -- is super-useful for peloponnese planning. Click & it gets huge -- naivigate w side-slides. Great stuff right on Way. BIG GREEN ROAD bypasses Athens, nonstop until Corinth Canal. Jump off at Isthmus, go out on Old Bridge for awesome pix (its SO deep SO skinny). After Canal; on RH side is ANCIENT NEMEA just 5 mi off road.; "runner-up" to Olympia, well excavated -- stunnng stadium where u can race from starting blocks 2500 years old. http://nemeangames.org/ The "Revived Nemean Games" every 4 years draw thousands fo kids/adults world-wide to compete. NO Crowds; enjoy in 45 mins.
I HOPE that you have thoroughly read the superb noncomercial website -- http://www.visitnafplio.com/ -- everything to do sea eat IN Nafplio plus walks, ancient sites etc all around. Kids enjoy The "Castle" aspect... take a bronze-door elevator IN a rock cliff (yes! just like a cheesy sci-fi movie) to a parapet Wall -- Acronafplio... and a PARK at the very PEak of the Peninsula... look down on "town beach" (Arvanita)... then walk a path at foot of cliff to get there. ALL in website; click every link. Plus Palamidi.. a Gibralter looming over Old Town (Tip - drive up back way, expllore fortress, then ONE parent walks kids DOWN the 999 steps other parent drives car to the cafe at the bottom, to await). OTHER sites? Myceena is loooong site for kids, but TIRYNS, just 10 mins outside town, is a Huge-Rock Thrill to climb around on, and NO crowds. Ancient Theatre of Epidaurus is something all kids love (you can skip the acres of surrounding runis). On way back to town, Tolo beach, not crowdy in September. I love nearby tiny Cove of ASINE, just one taverna. where you can change clothes & have good food.
Wondering if Mystras & Momemvasia will thrill kids.... Mystras =scrambling down hill of deserted churches. Monemavasia = huge fortress on a rock on a causeway but also not a lot to do. Areopoli in the fall for kids? Atmospheric but not funfest. Beach relaxation? don't go to Navarino, haven of Richy-Rich... go to a hidden Gem ... Hotel ZOE, on the small perfect beach of Gialova, 10 miles N of Pylos - http://www.zoeresort.com/ - renamed as resort, but its still the wonderful family that created it. Most perfect beach in West Peloponnese ... and nearby, stuff to explore... castles on a causeway, a wildlife refuge just North..
Hoping this leaves u w 4 days -- drive drive back to Airport, drop car, get carservice to Central ATH hotel for 2 days sightseeing, one Magical day-trip to An island -- AEGINA. Go on Weekday, no crowds. Night before buy tix near hotel for open-deck ferry (avoid hydrofoils). Taxi to Piraeus (30 mins) & you'll have a great 1-hour "mini-cruise"... huge freighters, tiny sloops, 3-masters. Here's a photo-sequence of such a day-trip... http://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/ -- have a last greek swim, and a sunset sail back to Athens ... a great finale to your trip.