Inokashira Zoo Park (http://www.tokyo-zoo.net/sp/ino/ )is the perfect place for a family with smaller kids. Kids will not get bored because there is such an eclectic selection of exhibitions: nature park, small zoo, petting zoo, aquarium area, rides, playground. And the beauty of it is that it is all compact. It's a little bit of everything in a not overwhelmingly large park area. So, you're not running around everywhere. You can see everything in 2-3 hours.
Inokashira Zoo Park has a little bit of everything: guinea pig petting zoo, squirrel zone, very reasonably priced 50-100 yen pay-by-the-ride kiddie amusement park (teacups, train, merry go round, swings, etc.), a small zoo area including monkey mountain, foxes, badger,owls, mice, and the famous elephant from WW2, Hanako.
There is a playground with a small climbing wall and the traditional playground toys.
It's only 400 yen and kids are free. Rides are 50-100 yen. There's parking across the street from the zoo park. It's 800 meters from Inokashira Station.