The National Garden off Syntagma Square has a small zoo, several duck ponds, a playground, and lots of room to run around. There's also a Children's Library with books in English and some toys and coloring materials (adults are usually not allowed to stay with their children). The library is usually open Tuesday through Saturday from 8:30am to 3pm, and is closed in August. The National Garden is open from sunrise to well after sunset.
There are other small parks and gardens scattered throughout Athens, but the National Garden is the best for children. That said, if you're staying in Kolonaki, try Dexamini Square, which has a small playground and several cafes and is below the St. George Lycabettos hotel off Kleomenous.
The very impressive privately operated Attica Zoological Park tel. 210/663-4724; atticapark@internet.gr), Spata, is home to more than 2,000 birds from some 320 species, a butterfly garden, and a small farm; the zoo, which plans to add more exhibits, is open daily from 10am to 7pm and charges 8€ admission (4€ for children). The zoo is not far from the new airport at Spata; given the state of most airports in the summer, the zoo might seem an oasis of tranquility.
The ride up Mount Likavitos on the cable-car railway (teleferique) is often a hit with kids. It usually operates every 20 minutes in summer (2€. There's a cafe on top that sells ice cream, and children can let off steam by running along any number of paths downhill.
A good place to check to see if there are any special activities going on is the Museum of Greek Children's Art, 9 Kodrou, Plaka (tel. 210/331-2621), where admission is 2€. It's open Tuesday through Saturday from 10am to 2pm and Sunday from 11am to 2pm; closed in August. This small museum has changing displays of children's art from throughout Greece, and your children may enjoy seeing what Greek kids like to draw. Workshops for children are offered (and conducted in Greek). There are also workshops at the Children's Museum, around the corner at 14 Kidathineon, but usually no exhibitions. In addition, there are sometimes Karaghiozis Puppet Shows (shadow theater) a few doors away at the Greek Folk Art Museum, 17 Kidathineon. You don't need to understand Greek to appreciate the slapstick comedy of Karaghiozis.
The multimedia center Hellenic Cosmos was founded in 1998 by the Foundation for the Hellenic World, 254 Pireos, Tavros (tel. 210/342-2292 or 210/483-5300; fax 210/342-2272; www.hellenic-cosmos.gr). It's open Monday, Tuesday, and Thursday from 9am to 6pm, Wednesday and Friday from 9am to 9pm, and Saturday and Sunday from 11am to 3pm; at press time, admission was free, with rumors of a fee in the offing. The interactive exhibits focus on Greek history and culture through the ages and draw lots of children. You can visit ancient Miletus on a virtual reality tour, browse the Web in the Internet cafe, and, more traditionally, see a collection of Greek costumes. Kalithea is the nearest Metro stop (a 10-minute walk away), but if you're bringing small children, you might want to take a taxi to avoid the walk.
There are usually lots of new-release American movies showing in central Athens, and a couple of hours in an air-conditioned theater is not a bad way to pass a hot afternoon. Check the English-language daily Athens News (www.athensnews.gr) or the daily Kathimerini insert in the International Herald Tribune for listings.
The "Scope" section in the weekly Hellenic Times lists activities of interest to children in Athens, including Girl Scout meetings, hiking excursions, and day camps, in its "Kids Corner."