are there swimming pools or gyms open to the public in the city? i'd do anything to shoot some hoops or go for a swim.

of course they are!
Spain is a public country, most things are owned by the country or by the city and everyone can go and swim, you have to pay a little ticket, maybe 200 or 300.
And for the basketball things you would not have to pay anything, there are basketball courts in some parks outdoors.

that sounds excellent! but what are the names of these places to play basketball indoors or swim? any information would be appreciated.

the basketball places are usually outdoors, and they are located in some parks in the city. just ask to anyone in your neighbourhood... ¿hay algún polideportivo por aquí o alguna chancha de baloncesto?
they will know.
the swimming thing, maybe in the university there's a swimming pool, ask there. pool is piscina, for sure there will be some pools in Madrid indoors and open to public. you could ask in the tourist office.

[This message has been edited by Antonio (edited 02-05-2001).]

According to Baedecker's MADRID, there are 150 swimming baths in Madrid. Baedecker's lists about 30 of them. Ones with which I am familiar are Lago and Canoe. I think Canoe (pronounced can oh é) may be 'members only.'

Canoe is a swimming team club. I am sure they will have some place and time for the public, it is always like that, members may swim for free, and regular public may have to pay 200 or 300 or a pass for 10 times or whatever they want.