Athens
Syntagma Square
Syntagma (Sindagma) Square - Kids will enjoy watching the changing of the guard in front of the Tomb of the Unknown Solider at the Parliament Building. On the hour, soldiers wearing traditional Greek costume with pleated kilt, embroidered jacket, red hat and clogs, precisely step into position.
National Gardens - The National Gardens is a big dusty green garden with gravel paths, snack bars, benches for picnicking, a duck pond (it's fun to watch the scads of ducks), room for kids to stretch their legs, and a big playground with swings, climbing structures, sandbox and those go-round things.
Temple of Olympian Zeus - Run down the length of the National Gardens, past the Zappio, and you'll stop at the archeological ruins of the Temple of Olympian Zeus. Erected over an ancient sacred spot, this temple is a Roman special (Emperor Hadrian called himself the Olympian Zeus). Only 15 columns still stand, but you can imagine what is was like with 104 columns supporting the temple roof - it was humongous.
Also, check out Hadrian's Arch, with two inscriptions, "This is the city of Hadrian, not Theseus," on the Roman facing side, and "This is Athens, the ancient city of Theseus," on the side that faces the Acropolis. (At this location, you're only a few blocks from the south side of the Acropolis.)