San Telmo is fine during the day and even at night (depending on the area.) My gym is in San Telmo, Balcarse and Venezuela. Also the Buenos Aires Museum of Modern Art in San Telmo. The Sunday Flee Market on Defensa Street is a real hoot.
The street is closed off to traffic from Plaza de Mayo to Ave. San Juan.
Also on Saturdays there's a Green Market on Balcarse between Chile and Mexico street where you can get everything fresh from the farms.
It closes at 2PM so you have to get there relatively early. Have fun.
YASMIN, if you're staying for a month, I'd recommend looking for something in another neighborhood like Palermo or Belgrano. Not only is it safer at night, I think you'll find it generally easier for day-to-day living... more grocery store, cafes, bakeries, etc. You'll see more of what daily BsAs life is like and not be eternally in a tourist trap full of nothing but other foreigners and pricing accordingly. Palermo has dozens of beautiful parks, lots of walkable avenues for shopping, the public transport is readily available in any direction, and you'll probably find a place to stay that's cheaper. And likely to be more modern and air-conditioned. Unless you like and want something "historic" (which can be beautiful, just not in the heat of summer, but maybe that's just me!)