I go to one on Chenaut between Baez and Campos (2 blocks from you). I don't know what you do at the gym -- this one isn't great if you like bikes as they only have low-riders. But I do weights and cardio and it's fine. For just the weights and the use of the treadmills, low-riders, elliptical it's $80 pesos a month (this will go up in Jan I'm sure). For $110 you can get the above + spinning x 2 a week. They also have a full range of martial arts classes, baile arabe etc.
There's another gym on Soldado de la Independencia and Ortega y Gasset (about 3 blocks) -- I checked it out but it was tiny. There's also ones on Campos between Chenaut and Arevalo, and one on Matienzo at about Soldado de la Independencia. I don't know about these ones but you can walk by and see.
The biggest one in this end of Canitas is Magic Gym -- they have a huge range of aerobic machines, a large musculacion room, 3 tennis courts, and a pool (that's yucky and crowded in the summer, but if you don't have a pool it might be nice to have the option). I don't know what Magic's rates are now, a couple of years ago they were 100 pesos +, so I assume more, but I don't know what that included. Magic entrance is on Dorrego I think the cross is Huergo but I can't remember -- if you walk along Baez in the direction of Dorrego and hang a right, you'll eventually come to it.