Tokyo Playgrounds

Do parks in Tokyo typically have playgrounds and climbing structures for little ones?

In particular:

Hibiya Park
Yoyogi Park
Shinjuku Gyoen
Shinjuku Central Park

There large, inner city parks do not have play areas for children as far as I know unfortunately. Hibiya Park is more of an old-fashioned formal garden-park without grassy areas, and Shinjuku Central Park has a large resident homeless population, so not a place I'd take kids. Shinjuku Gyoen and Yoyogi have ponds, large expanses of grass and lots of trees, but no climbing frames that I've ever seen.

Some smaller inner city parks nearer to residential areas rather than the commercial areas you have mentioned have children's play areas. Out in the suburbs almost all parks have various climbing frames and facilities for kids- a good one is Koganei Park, but it is a bit of a hike if you are staying in central Tokyo.

Michael,

By Central Park, do you mean Shinjuku Chuo Koen in Shinuku Fukutoshin area? If so, they have a children's playground with swings, slides and toilets as well as a pond the kids can dip their legs into. Ask for "Chibikko Hiroba (which means 'kid's square')" which is the left upper area of the following map. The right-hand side is the grassy area, by the way.
http://parkandcats.hp.infoseek.co.jp/sinzyukutyuoukouen.html

The other three parks may not have structures, but they all have plenty of space for little children to run around, and as Sira suggested, is located in the better part of the city. It's just that all these major parks are so big that it may be difficult to reach the right spot unless you ask people for directions.

The following website may help you find more parks that suit your needs. The site also shows maps of the parks you've mentioned.
http://www.tokyo-park.or.jp/english/index.html

I read some of the department stores have playgrounds on the roof. Which ones?

I know two:
Keio Department Store @Shinjuku
Seibu Department Store @Ikebukuru

Thanks! I did a Google Earth view, pointing it at the Keio in Shinjuku. A lot easier to look at now!

http://www.flickr.com/photos/unforth/1436641275/