Art and Culture
BA’s Museo de Bellas Artes (Museum of Fine Arts) is always free, and its permanent collection features works by masters such as Degas, Gauguin, Klee, Kandinsky, and Van Gogh as well as Argentinian and South American artists.
Museo de Arte Latinoamericano de Buenos Aires (Museum of Latin American Art), known more commonly by its acronym MALBA, is free every Wednesday. Take advantage of this free day to take in some of the museum’s 200 pieces of painting, sculpture, drawings, and photos from the 20th century to today, featuring such Latin American artists as Kahlo, Rivera, Clark, and Torres-García, among many others.

Free Tours
Buenos Aires’s official tourism site offers downloadable maps and step-by-step instructions for 18 self-guided tours that traverse the city and introduce visitors to the city’s history, sites and sounds. The neighborhoods covered are Abasto, Av. De Mayo, Av. Corrientes Belgrano, Catedral, Barracas, La Boca, Corrientes, Nueva Pompeya, Boedo, Caballito, Monserrat, Plaza Lavalle, Puerto Madero, Recoleta, retiro, San Telmo and Palermo. There are also three biographical tours of Eva Perón (Evita), Jorge Luis Borges, tango great Carlos Gardel. You can download these maps at http://www.bue.gov.ar/recorridos
The BA Tourism Bureau also puts on free, guided tours through the city that focus on its history and architecture, but they are in Spanish only. Check out at http://www.bue.gov.ar/recorridos/index.php?menu_id=17&info=visitas&lang=en

Outdoors
I recommend you to visit the Reserva Ecológica Costanera Sur (Ecological Reserve). Opened in 1918 and restored in the 1990s, this 350-acre park is a quiet place to stroll, bike, or enjoy a picnic lunch all the while taking in the beautiful view of the city’s skyline. From there you can see the buildings of Puerto Madero.
Another option are the Bosques de Palermo (Forests of Palermo), an urban oasis close to 200 acres in size, featuring two artificial lakes and 12,000 trees. Stop and smell the roses at the park’s El Rosedal, a roses´s garden.
You can also visit the Jardín Botánico Carlos Thays (the Carlos Thays Botanical Garden) in Palermo which covers over 17 acres of green space and contains more than 6,000 plant species. Free guided tours in English take place Fridays at 1 p.m. Tours in Spanish are offered more often: Fridays at 10:30 and Saturdays, Sundays, and holidays at 10:30 and 3 p.m.