Athens
Lycabettus (Lycavitos)
Lycabettus (Lykavitos) Hill - Take cable car (funicular) to the top of Lykavitos Hill, for a fabulous view of Athens all around. (The cable car runs 9 - 3 daily.) Stop at the cafe for a snack, then kids can walk down (run down) the zig zag path to the bottom (it's not that far).
If you have little kids, at Plateia Dexameni there's a small but nice playground, with climbing structures under the orange trees.
Benaki Museum - The Benaki Museum is a gem - it encompasses the history of Greece from antiquity to independence in the 19th century. There are displays of classical Greek vases, gold jewelry, Byzantine icons and mosaics, and an incredible costume collection from all over Greece - fabrics in sumptuous rich colors, gorgeously embroidered, layers of vests and long skirts, and sparkling pointy-toed slippers. On the top floor, you'll find swords, rifles and silver-crusted pistols from the war of independence, and a lovely cafe that's perfect for a lunch break.
Museum of Cycladic Art - A small museum with a great collection of the most ancient Greek art, figurines with arms folded across their tummies. The Cycladic figures are shrouded in mystery - they might be fertility goddesses, or even toys. Also, check out the Greek vases, bronze helmets, gold jewelry, and tiny ceramic votive figures. In the basement is a touch table with replicas of the Cycladic figurines.
War Museum of Greece - Nice collection of Turkish scimitars, blunderbuses, beautifully decorated European hunting rifles, Arabian daggers, Cossack pistols, French nobleman swords, plus World War II stuff. Outside the museums there are cannons, field guns, a "mobile armored carriage" and old airplanes.
(This museum isn't far from the Benaki Museum, so if you have one kid who want to looks at war stuff, and another who wants to see costumes, you've something for both.)