ok. you want to steer clear of the tourist trap, glitzy gyms like megatlon. i have trained in gyms over the years since i was 22, and when i was in argentina living for 6 months, i was training the most of my life, doing 2 classes a day. i can thoroughly recommend magic center club, which is in last canitas, not too far from palermo, Dorrego 2880, between luis maria campos and huergo. it's an indpendent gym, and although situated in a 'trendy' area, it's probably still significantly cheaper than megatlon, and has loads of classes of all types, from yoga and pilates to kickboxing and weightraining throughout the day. i joined megatlon last time i was there, and the monthly membership price was astranomical, and the classes i felt were mediocre at best, plus, because it's expensive, the clientelle tend to be nuveau riche and ultra body conscious. i just didn't feel comfortable training there to be honest, and i was at the belgrano branch.
check out magic, you might like it. they have a mini pool upstairs, great for a cool down dip. and they are a tennis club, so plenty of opportunities to hone those skills, if you want to add that to your membership as well.
www.magiccenter.com.ar
good luck.