The Buenos Aires Tourist Board office is, unfortunately, not open to visitors; however, you should have no difficulty finding little kiosks throughout the city where you can get free maps and information to help you navigate.

There is also a hotline for tourism information: 11/4313-0187.

The Buenos Aires Tourist Bureau has a very comprehensive and informative web page where you can find all sorts of information

And as for actual tourist offices that offer maps and pamphlets and people to ask questions to here is a list (taken from the Tourist Bureau web pages.) I personally have used the one in San Telmo - so can vouch that it is open to the public.

 7 centros de información turística    
Aeroparque Internacional Ministro Pistarini, Espigón Internacional 
Address: Ezeiza 
Neighborhood: Pcia. de Buenos Aires 
Hours: lunes a viernes de 10 a 17.  
Aeroparque Jorge Newbery 
Address: Hall central de Aerolíneas Argentinas 
Neighborhood: Palermo 
 (54 11) 4771 0104 
Hours: lunes a domingos de 10 a 17.  
Address: Florida 100 
Neighborhood: San Nicolás 
 (54 11) 4313 0187 
Hours: lunes a viernes de 9 a 18; sábados de 10 a 16. 
Puerto Madero 
Address: Alicia Moreau De Justo 200 Dique 4 
Neighborhood: Puerto Madero 
 (54 11) 4313 0187 
Hours: lunes a domingos de 10 a 18. En este centro también se ofrece información de la ciudad de Montevideo, Uruguay.  
Address: Quintana 596 
Neighborhood: Recoleta 
 (54 11) 4313 0187 
Hours: lunes a domingos de 10 a 18 hs.  
Address: Av. Antártida Argentina (Terminal de ómnibus Local 83) 
Neighborhood: Retiro 
 ( 54 11) 4311 0528 
Hours: lunes a sábados de 7.30 a 13.  
San Telmo 
Address: Defensa 1250 
Neighborhood: San Telmo 
 (54 11) 4313 0187 
Hours: sábados y domingos de 10 a 18