During the 19th century, BA grew from a glorified smugglers' den on the fringes of the Spanish empire into one of the biggest, richest and most culturally influential cities in the Americas. From 1860 onwards, a vast grid spread out from the civic heart at the Casa Rosada on Plaza de Mayo and grand boulevards were laid in homage to competition with the Haussman of Paris. Just south of the political HQs are the old city barrios of San Telmo and La Boca where the boats came in to unload Italian immigrants and left with salt beef and hides. Tango has its origins here around the 1900s and La Boca's technicolour Caminito Street celebrates a classic song from tango's golden age.

Take a stroll round Recoleta, north of the centre, and you will be struck by the opulent residences in which the well-born live, and die. The Cementerio de la Recoleta (Junín 1760, +541148031594), an eerily opulent necropolis of marble mausoleums and statuary, is the Argentinian capital's most famous landmark. The nearby Museo de Bellas Artes (Avenida del Libertador 1473, +541148030802, www.mnba.com.ar) is strong on porteño painting - look out for vivid, social realist collages by Antonio Berni and the tango-inspired figures of Antonio Segui. This is also a district of beautiful plazas, parks and monuments.

To get your bearings for the rest of the city, the Obelisco is a good starting point; it's bang in the middle of the world's widest avenue, 9 de Julio. East of here is Puerto Madero, traditional gateway to the Rio de la Plata, now spruced up into BA's newest and most development-intensive barrio. Here you can lunch in world-class steakhouses like Cabana Las Lilas while watching the yachts glide by, or simply take a dusk stroll along the promenade. West of the Obelisco - up the main theatre drag, Avenida Corrientes - is the Abasto, a former-market-turned-shopping mall in an area of temples and tango shows honouring the memory of Carlos Gardel, tango's most famous crooner. At the Museo Casa Carlos Gardel (Jean Jaurès 735, +541149642071), music and memorabilia are on display in his mother's old house and a glitzy floorshow, La Esquina de Carlos Gardel (Pasaje Carlos Gardel 3200, +541148676363, www.esquinacarlosgardel.com.ar), pulls in hordes of tangoing tourists.

So much for classic BA. Some of the quirkier, more cutting-edge additions to BA's dynamic cultural scene are equally enthralling. At the Malba modern art museum (Avenida Figueroa Alcorta 3415, +541148086500, www.malba.org.ar), the local Saatchi, Eduardo Costantini, has made public his important collection of 20th-century art from all over Latin America, including Frida Kahlo, Tarsila do Amaral and Xul Solar. Other key spaces include the Centro Cultural Borges (Galerias Pacifico, Viamonte and San Martín, +541155555440, www.ccborges.org.ar), which has recently hosted exhibitions featuring Cartier-Bresson and Andy Warhol; and Proa, in La Boca (Avenida Pedro de Mendoza 1929, +541143030909, www.proa.org), whose pointedly eclectic programmes often feature indigenous South American art. If you prefer to pay homage to more contemporary icons, head round the corner to Museo de la Pasión Boquense (Brandsen 805, +541143621100, www.museoboquense.com) where Diego Maradona and other footballing heroes who have passed through Boca Juniors FC are idolised.

Since the peso was devalued three years ago, pounds, euros and dollars get you a lot of steak, fun, leather, wine or whatever else you are looking for. Long a mere stopover for adventure tourists bound for Andean parks and the Iguazú Falls, BA is worth a visit for itself - it is exciting, entertaining and an education too.