Try this link. It should take you to a list of all the pools around town. Your best bet is probably the municipal pool at Lago, in the Casa de Campo. Cheap and cheerful. For a quieter day out, fewer children and so on, try the private pool called Stella, in Arturo Soria. It's more expensive. And if you really want to splash out, head for the spectacular roof-top pool in the Hotel Emperador on the Gran Via. It's really expensive.
http://www.guiademadrid.com/guia/n_deporte/base.asp?Tipo=piscinas