The Feria Plaza Francia, officially known as the Intendente Alvear Artisan Fair, is an crafts market that takes place every weekend in the plaza in front of the Recoleta Cemetery. Since so many markets in Buenos Aires take place only on Sunday (Mataderos and San Telmo, for example), I recommend coming here on a Saturday and saving your Sunday for one of the others.
The booths here sell great souvenirs including jewelry, paintings, carved serving platters, and clothing.
Open on Saturdays, Sundays, and holidays from 10 am to 8 pm (officially, but aim for closer to noon as Argentines are not exactly early risers).