For Barnaby -
In Palermo there is a gym in the Alto Palermo shopping complex.
They have an outside entrance for early arrivals. We used it for three months and found it to be clean, well laid out and all the machinery worked. They also have shower facilities and lockers to store your stuff when working out.
My wife said her changing room had the same facilities and was very clean as well.
The gym shares the air conditioning with the shopping part of the building and when it gets really warm, the shops take as much of the cool air as they can get, and the gym gets a little warm. Other than that, it's fine.
It's easy to get to - Bulnes station on the green subte line (in Palermo).
They were very nice about allowing "visitors" short term use of the facility. Cost us a total of 540 pesos (270 each) for the three months that we were there.
if you need more info about the Palermo area, send a PM and I'll fill you in. We lived there for awhile.
It's a really great part of the city - personally I think the best ... and definitely better than San Telmo or La Boca.