I second stanbr's recommendation of Mystras. We were in Greece this past May. We spent 5 nights in Nafplion, which is beautiful. We saw spectacular sunsets while in Nafplion. Of all the ruins we visited, Mystras is my favorite. I would love to return because we didn't have time to visit all of the Lower Town. I think your children will love the Upper Town. You can hike to the top of the castle remains for spectacular views. I am 72 so it was a bit strenuous for me but should be easier for younger people. Please be sure to wear very sturdy walking shoes/sneakers. You didn't say what time of year. If it's during warm weather months, you must have sunscreen, hats, sunglasses and plenty of water.
We stayed in Omorfi Poli in Nafplion and loved our stay there. Their breakfast buffet is delicious, and the central location is very convenient. They have a lovely outdoor dining area.
We followed the Micheline Green Guide for a walking tour of Nafplio. Also spent 3 hours at Arvanita Beach one day. Visited Epidaurus and Mycenae which we enjoyed but our favorite is Mystras for ruins.