Bel Canto takes place in the vice president's residence in an unnamed South American country. There is good reason to think, however, that the country is Peru and the city is Lima:
2. The "host country" is described as "a poor country", "mad for soap operas", farming "coca leaves and blackhearted poppies". It has a president of Japanese ethnicity and the maids are "Indian". The "south of the country" is "near the ocean".
3. The capital is "not far from the jungle" and is afflicted by the garúa, "more than mist and less than drizzle", "from April through November".
4. The domestic terrorists speak Quechua, and refer to a "high-altitude prison".
Quechua is spoken in Peru, Bolivia, Colombia, Ecuador, Chile and Argentina. But Bolivia is land-locked, and Colombia and Ecuador have inland southern regions. Chile is not generally considered a poor country. Most coca is grown in Colombia, Peru and Bolivia. The garúa is found on the lower western slopes of the Andes, where Lima is situated. Argentina's capital, Buenos Aires, is on the opposite side of the continent. Peru has a large ethnic Japanese population, and at the time Patchett was writing had an ethnically Japanese president. The country has both jungle and high-altitude terrain. Soap operas are very popular in Peru.
Admittedly, Lima is not particularly close to "the jungle", and it is odd that there is no mention of the coast. However, no other Latin capital fits the bill, so we can conclude that Patchett's unnamed capital is, or is based on, Lima.
Founded in 1535 by the conquistador Francisco Pizarro, Lima is now the fifth largest city in Latin America, with around 9 million inhabitants. It is situated in a desert at the foot of the Andes, on the Pacific coast.
Lima has been devastated by earthquakes at various points in its long history, but still has plenty of fine colonial architecture. The historic centre is a UNESCO World Heritage Site.